initial commit / add all books

23 files changed, 885 insertions, 0 deletions

diff --git a/1670/CH3/EX3.1/3_1.sce b/1670/CH3/EX3.1/3_1.sce
new file mode 100755
index 000000000..b932372bf
--- /dev/null
+++ b/1670/CH3/EX3.1/3_1.sce
@@ -0,0 +1,9 @@
+//Example 3.1

+//Direct Method

+//Page no. 3.1

+clc;clear;close;

+

+A=[1,1,2;1,2,3;2,3,1];         //Parameter Matrix

+B=[1;1;2]

+C=inv(A)*B;

+disp(C,"Solution Matrix = ")
\ No newline at end of file
diff --git a/1670/CH3/EX3.10/3_10.sce b/1670/CH3/EX3.10/3_10.sce
new file mode 100755
index 000000000..5c707aadf
--- /dev/null
+++ b/1670/CH3/EX3.10/3_10.sce
@@ -0,0 +1,56 @@
+//Example 3.10

+//Triangularization Method

+//Page no. 62

+clc;clear;close;

+

+A=[2,4,-6;1,5,3;1,3,2];

+B=[-4;10;5];

+printf('A can be factorizaed as follows:\n')

+printf('\tL\t\t  *\t\tU\t\t  =\t\tA')

+U(2,1)=0;U(3,1)=0;U(3,2)=0;

+L(1,2)=0;L(1,3)=0;L(2,3)=0;

+for i=1:3

+    L(i,i)=1

+end

+for i=1:3

+    U(1,i)=A(1,i)

+end

+L(2,1)=1/U(1,1);

+for i=2:3

+    U(2,i)=A(2,i)-U(1,i)*L(2,1);

+end

+L(3,1)=1/U(1,1);

+L(3,2)=(A(3,2)-U(1,2)*L(3,1))/U(2,2);

+U(3,3)=A(3,3)-U(1,3)*L(3,1)-U(2,3)*L(3,2);

+printf('\n')

+for i=1:3

+    for j=1:3

+        printf('%.2f\t',L(i,j))

+    end

+    

+    if(i==2)

+        printf('  *     ')

+    else

+        printf('\t')

+    end

+    

+    for j=1:3

+        printf('%.2f\t',U(i,j))

+    end

+    if(i==2)

+        printf('  =     ')

+    else

+        printf('\t')

+    end

+    for j=1:3

+        printf('%.2f\t',A(i,j))

+    end

+    printf('\n')

+end

+printf('\nY=U*X')

+    Y=inv(L)*B

+    X=inv(U)*Y

+printf('\n\nX=')

+for i=1:3

+    printf('\n   %i',X(i,1))

+end
\ No newline at end of file
diff --git a/1670/CH3/EX3.11/3_11.sce b/1670/CH3/EX3.11/3_11.sce
new file mode 100755
index 000000000..cd43b2052
--- /dev/null
+++ b/1670/CH3/EX3.11/3_11.sce
@@ -0,0 +1,56 @@
+//Example 3.11

+//Triangularization Method

+//Page no. 63

+clc;clear;close;

+

+A=[1,3,8;1,4,3;1,3,4];

+B=[4;-2;1];

+printf('A can be factorizaed as follows:\n')

+printf('\tL\t\t  *\t\tU\t\t  =\t\tA')

+U(2,1)=0;U(3,1)=0;U(3,2)=0;

+L(1,2)=0;L(1,3)=0;L(2,3)=0;

+for i=1:3

+    L(i,i)=1

+end

+for i=1:3

+    U(1,i)=A(1,i)

+end

+L(2,1)=1/U(1,1);

+for i=2:3

+    U(2,i)=A(2,i)-U(1,i)*L(2,1);

+end

+L(3,1)=1/U(1,1);

+L(3,2)=(A(3,2)-U(1,2)*L(3,1))/U(2,2);

+U(3,3)=A(3,3)-U(1,3)*L(3,1)-U(2,3)*L(3,2);

+printf('\n')

+for i=1:3

+    for j=1:3

+        printf('%.2f\t',L(i,j))

+    end

+    

+    if(i==2)

+        printf('  *     ')

+    else

+        printf('\t')

+    end

+    

+    for j=1:3

+        printf('%.2f\t',U(i,j))

+    end

+    if(i==2)

+        printf('  =     ')

+    else

+        printf('\t')

+    end

+    for j=1:3

+        printf('%.2f\t',A(i,j))

+    end

+    printf('\n')

+end

+printf('\nY=U*X')

+    Y=inv(L)*B

+    X=inv(U)*Y

+printf('\n\nX=')

+for i=1:3

+    printf('\n   %.2f',X(i,1))

+end
\ No newline at end of file
diff --git a/1670/CH3/EX3.12/3_12.sce b/1670/CH3/EX3.12/3_12.sce
new file mode 100755
index 000000000..9ca063351
--- /dev/null
+++ b/1670/CH3/EX3.12/3_12.sce
@@ -0,0 +1,56 @@
+//Example 3.12

+//Triangularization Method

+//Page no. 63

+clc;clear;close;

+

+A=[4,-1,2;-1,5,3;2,3,6];

+B=[12;10;18];

+printf('A can be factorizaed as follows:\n')

+printf('\tL\t\t  *\t\tU\t\t  =\t\tA')

+U(2,1)=0;U(3,1)=0;U(3,2)=0;

+L(1,2)=0;L(1,3)=0;L(2,3)=0;

+for i=1:3

+    L(i,i)=1

+end

+for i=1:3

+    U(1,i)=A(1,i)

+end

+L(2,1)=1/U(1,1);

+for i=2:3

+    U(2,i)=A(2,i)-U(1,i)*L(2,1);

+end

+L(3,1)=1/U(1,1);

+L(3,2)=(A(3,2)-U(1,2)*L(3,1))/U(2,2);

+U(3,3)=A(3,3)-U(1,3)*L(3,1)-U(2,3)*L(3,2);

+printf('\n')

+for i=1:3

+    for j=1:3

+        printf('%.2f\t',L(i,j))

+    end

+    

+    if(i==2)

+        printf('  *     ')

+    else

+        printf('\t')

+    end

+    

+    for j=1:3

+        printf('%.2f\t',U(i,j))

+    end

+    if(i==2)

+        printf('  =     ')

+    else

+        printf('\t')

+    end

+    for j=1:3

+        printf('%.2f\t',A(i,j))

+    end

+    printf('\n')

+end

+printf('\nY=U*X')

+    Y=inv(L)*B

+    X=inv(U)*Y

+printf('\n\nX=')

+for i=1:3

+    printf('\n   %.2f',X(i,1))

+end
\ No newline at end of file
diff --git a/1670/CH3/EX3.13/3_13.sce b/1670/CH3/EX3.13/3_13.sce
new file mode 100755
index 000000000..3b089c210
--- /dev/null
+++ b/1670/CH3/EX3.13/3_13.sce
@@ -0,0 +1,48 @@
+//Example 3.13

+//Crout Method

+//Page no. 67

+clc;clear;close;

+

+A=[1,2,3,1;3,1,1,0;2,1,1,0]

+for i=1:3

+    for j=1:4

+        if j==1 then

+            M(i,j)=A(i,j)

+        elseif i==1

+            M(i,j)=A(i,j)/A(1,1)

+        elseif j==2

+            M(i,j)=A(i,j)-M(1,j)*M(i,j-1)

+        elseif i==2

+            M(i,j)=(A(i,j)-M(i,1)*M(i-1,j))/M(i,2)

+        elseif j==3

+            M(i,j)=A(i,j)-(M(i,j-2)*M(i-2,j)+M(i,j-1)*M(i-1,j))

+        else

+            M(i,j)=(A(i,j)-(M(i,j-3)*M(i-2,j)+M(i,j-2)*M(i-1,j)))/M(i,j-1)

+        end

+    end

+end

+disp(M,'M = ')

+for i=1:3

+    for j=1:4

+        if j~=4 then

+            U1(i,j)=M(i,j)

+        else

+            Y(i,1)=M(i,j)

+        end

+    end

+end

+U=eye(3,3)

+for i=1:3

+    for j=1:3

+        if j>i then

+            U(i,j)=U1(i,j)

+        end

+    end

+end

+disp(U,'U = ')

+disp(Y,'Y = ')

+X=inv(U)*Y

+printf('\n\nHence, the solution is : \t')

+for i=1:3

+    printf('x%i = %i\t\t',i,X(i))

+end
\ No newline at end of file
diff --git a/1670/CH3/EX3.14/3_14.sce b/1670/CH3/EX3.14/3_14.sce
new file mode 100755
index 000000000..9234ca063
--- /dev/null
+++ b/1670/CH3/EX3.14/3_14.sce
@@ -0,0 +1,48 @@
+//Example 3.14

+//Crout Method

+//Page no. 68

+clc;clear;close;

+

+A=[2,1,4,12;8,-3,2,20;4,11,-1,33]

+for i=1:3

+    for j=1:4

+        if j==1 then

+            M(i,j)=A(i,j)

+        elseif i==1

+            M(i,j)=A(i,j)/A(1,1)

+        elseif j==2

+            M(i,j)=A(i,j)-M(1,j)*M(i,j-1)

+        elseif i==2

+            M(i,j)=(A(i,j)-M(i,1)*M(i-1,j))/M(i,2)

+        elseif j==3

+            M(i,j)=A(i,j)-(M(i,j-2)*M(i-2,j)+M(i,j-1)*M(i-1,j))

+        else

+            M(i,j)=(A(i,j)-(M(i,j-3)*M(i-2,j)+M(i,j-2)*M(i-1,j)))/M(i,j-1)

+        end

+    end

+end

+disp(M,'M = ')

+for i=1:3

+    for j=1:4

+        if j~=4 then

+            U1(i,j)=M(i,j)

+        else

+            Y(i,1)=M(i,j)

+        end

+    end

+end

+U=eye(3,3)

+for i=1:3

+    for j=1:3

+        if j>i then

+            U(i,j)=U1(i,j)

+        end

+    end

+end

+disp(U,'U = ')

+disp(Y,'Y = ')

+X=inv(U)*Y

+printf('\n\nHence, the solution is : \t')

+for i=1:3

+    printf('x%i = %i\t\t',i,X(i))

+end
\ No newline at end of file
diff --git a/1670/CH3/EX3.15/3_15.sce b/1670/CH3/EX3.15/3_15.sce
new file mode 100755
index 000000000..8a2e3aaea
--- /dev/null
+++ b/1670/CH3/EX3.15/3_15.sce
@@ -0,0 +1,52 @@
+//Example 3.15

+//Crout Method

+//Page no. 69

+clc;clear;close;

+

+A=[1,2,-12,8,27;5,4,7,-2,4;-3,7,9,5,11;6,-12,-8,3,49]

+for i=1:4

+    for j=1:5

+        if j==1 then

+            M(i,j)=A(i,j)

+        elseif i==1

+            M(i,j)=A(i,j)/A(1,1)

+        elseif j==2

+            M(i,j)=A(i,j)-M(1,j)*M(i,j-1)

+        elseif i==2

+            M(i,j)=(A(i,j)-M(i,1)*M(i-1,j))/M(i,2)

+        elseif j==3

+            M(i,j)=A(i,j)-(M(i,j-2)*M(1,j)+M(i,j-1)*M(2,j))

+        elseif i==3

+            M(i,j)=(A(i,j)-(M(i,1)*M(i-2,j)+M(i,2)*M(i-1,j)))/M(i,3)

+        elseif j==4

+            M(i,j)=A(i,j)-(M(i,j-2)*M(i-2,j)+M(i,j-1)*M(i-1,j)+M(i,j-3)*M(i-3,j))

+        else

+            M(i,j)=(A(i,j)-(M(i,j-2)*M(i-1,j)+M(i,j-3)*M(i-2,j)+M(i,j-4)*M(i-3,j)))/M(i,j-1)

+        end

+    end

+end

+disp(M,'M = ')

+for i=1:4

+    for j=1:5

+        if j~=5 then

+            U1(i,j)=M(i,j)

+        else

+            Y(i,1)=M(i,j)

+        end

+    end

+end

+U=eye(4,4)

+for i=1:4

+    for j=1:4

+        if j>i then

+            U(i,j)=U1(i,j)

+        end

+    end

+end

+disp(U,'U = ')

+disp(Y,'Y = ')

+X=inv(U)*Y

+printf('\n\nHence, the solution is : \t')

+for i=1:4

+    printf('x%i = %i  \t',i,X(i))

+end
\ No newline at end of file
diff --git a/1670/CH3/EX3.16/3_16.sce b/1670/CH3/EX3.16/3_16.sce
new file mode 100755
index 000000000..d9ec058ab
--- /dev/null
+++ b/1670/CH3/EX3.16/3_16.sce
@@ -0,0 +1,17 @@
+//Example 3.16

+//Jacobi Method

+//Page no. 72

+clc;clear;close;

+

+x0=0;y0=0;z0=0;

+deff('x=f1(y,z)','x=(y-z+10)/5')

+deff('y=f2(x,z)','y=(-2*x+z+11)/8')

+deff('z=f3(x,y)','z=(x-y+3)/4')

+for i=1:13

+    x1=f1(y0,z0);

+    y1=f2(x0,z0);

+    z1=f3(x0,y0);

+    printf('\tx(%i) = %g\n\n\ty(%i) = %g\n\n\tz(%i) = %g\n\n\n\n',i,x1,i,y1,i,z1)

+    x0=x1;y0=y1;z0=z1;

+end

+printf('Thus we find that solution converges to %g,%g and %g',x0,y0,z0)
\ No newline at end of file
diff --git a/1670/CH3/EX3.17/3_17.sce b/1670/CH3/EX3.17/3_17.sce
new file mode 100755
index 000000000..f16181e6b
--- /dev/null
+++ b/1670/CH3/EX3.17/3_17.sce
@@ -0,0 +1,16 @@
+//Example 3.17

+//Gauss Seidel Method

+//Page no. 73

+clc;clear;close;

+

+x0=0;y0=0;z0=0;

+deff('x=f1(y,z)','x=(y-z+10)/5')

+deff('y=f2(x,z)','y=(-2*x+z+11)/8')

+deff('z=f3(x,y)','z=(x-y+3)/4')

+for i=1:8

+    x0=f1(y0,z0);

+    y0=f2(x0,z0);

+    z0=f3(x0,y0);

+    printf('\tx(%i) = %g\n\n\ty(%i) = %g\n\n\tz(%i) = %g\n\n\n\n',i,x0,i,y0,i,z0)

+end

+printf('Thus we find that solution converges to %g, %g and %g',x0,y0,z0)
\ No newline at end of file
diff --git a/1670/CH3/EX3.18/3_18.sce b/1670/CH3/EX3.18/3_18.sce
new file mode 100755
index 000000000..51713057d
--- /dev/null
+++ b/1670/CH3/EX3.18/3_18.sce
@@ -0,0 +1,16 @@
+//Example 3.18

+//Gauss Seidel Method

+//Page no. 74

+clc;clear;close;

+

+x0=0;y0=0;z0=0;

+deff('x=f1(y,z)','x=(110-y-z)/54')

+deff('y=f2(x,z)','y=(72-2*x-6*z)/15')

+deff('z=f3(x,y)','z=(85+x-6*y)/27')

+for i=1:5

+    x0=f1(y0,z0);

+    y0=f2(x0,z0);

+    z0=f3(x0,y0);

+    printf('\tx(%i) = %g\n\n\ty(%i) = %g\n\n\tz(%i) = %g\n\n\n\n',i,x0,i,y0,i,z0)

+end

+printf('Thus we find that solution converges to %.3f, %.3f and %.3f',x0,y0,z0)
\ No newline at end of file
diff --git a/1670/CH3/EX3.19/3_19.sce b/1670/CH3/EX3.19/3_19.sce
new file mode 100755
index 000000000..c142dcff2
--- /dev/null
+++ b/1670/CH3/EX3.19/3_19.sce
@@ -0,0 +1,16 @@
+//Example 3.19

+//Gauss Seidel Method

+//Page no. 75

+clc;clear;close;

+

+x0=0;y0=0;z0=0;

+deff('x=f1(y,z)','x=(32-4*y+z)/28')

+deff('y=f2(x,z)','y=(35-2*x-4*z)/17')

+deff('z=f3(x,y)','z=(24-x-3*y)/10')

+for i=1:6

+    x0=f1(y0,z0);

+    y0=f2(x0,z0);

+    z0=f3(x0,y0);

+    printf('\tx(%i) = %g\n\n\ty(%i) = %g\n\n\tz(%i) = %g\n\n\n\n',i,x0,i,y0,i,z0)

+end

+printf('Thus we find that solution converges to %.4f, %.4f and %.4f',x0,y0,z0)
\ No newline at end of file
diff --git a/1670/CH3/EX3.2/3_2.sce b/1670/CH3/EX3.2/3_2.sce
new file mode 100755
index 000000000..aae2b5970
--- /dev/null
+++ b/1670/CH3/EX3.2/3_2.sce
@@ -0,0 +1,36 @@
+//Example 3.2

+//Gaussian Elimination Method

+//Page no. 54

+clc;clear;close;

+

+A=[2,4,-6,-4;1,5,3,10;1,3,2,5];           //augmented matrix

+

+//triangularization

+for i=1:3

+    for j=1:4

+        if i==1 then

+            B(i,j)=A(i,j)

+        elseif i==2

+            B(i,j)=A(i,j)-A(i,1)*A(i-1,j)/A(1,1)

+            B(i+1,j)=A(i+1,j)-A(i+1,1)*A(i-1,j)/A(1,1)

+        elseif i==3

+            if j==1 then

+                A=B

+            end

+            B(i,j)=B(i,j)-A(i,2)*B(i-1,j)/B(2,2)

+        end

+    end

+end

+disp(A,'Augmented Matrix=')

+disp(B,'Triangulated Matrix=')

+//back substitution

+x(3)=B(3,4)/B(3,3);

+printf('\nx(3)= %i\n',x(3))

+for i=2:-1:1

+    k=0

+    for j=i+1:3

+       k=k+B(i,j)*x(j)

+    end

+    x(i)=(1/B(i,i))*(B(i,4)-k)

+     printf('\nx(%i)= %i\n',i,x(i))

+end

diff --git a/1670/CH3/EX3.20/3_20.sce b/1670/CH3/EX3.20/3_20.sce
new file mode 100755
index 000000000..5f8f0db43
--- /dev/null
+++ b/1670/CH3/EX3.20/3_20.sce
@@ -0,0 +1,16 @@
+//Example 3.20

+//Gauss Seidel Method

+//Page no. 75

+clc;clear;close;

+

+x0=0;y0=0;z0=0;

+deff('x=f1(y,z)','x=(17-y+2*z)/20')

+deff('y=f2(x,z)','y=(-18-3*x+z)/20')

+deff('z=f3(x,y)','z=(25-3*x+3*y)/20')

+for i=1:3

+    x0=f1(y0,z0);

+    y0=f2(x0,z0);

+    z0=f3(x0,y0);

+    printf('\tx(%i) = %g\n\n\ty(%i) = %g\n\n\tz(%i) = %g\n\n\n\n',i,x0,i,y0,i,z0)

+end

+printf('Thus we find that solution converges to %.1g, %.1g and %.1g',x0,y0,z0)
\ No newline at end of file
diff --git a/1670/CH3/EX3.21/3_21.sce b/1670/CH3/EX3.21/3_21.sce
new file mode 100755
index 000000000..335c80b6b
--- /dev/null
+++ b/1670/CH3/EX3.21/3_21.sce
@@ -0,0 +1,48 @@
+//Example 3.21

+//Relaxation Method

+//Page no. 79

+clc;clear;close;

+

+A=[10,-2,-2,-6;-1,10,-2,-7;-1,-1,10,-8]

+deff('y=R(i,x,y,z)','y=A(i,1)*x+A(i,2)*y+A(i,3)*z+A(i,4)')

+printf('dx\tdy\tdz\tdR1\tdR2\tdR3\n---------------------------------------------')

+I=eye(3,3)

+for i=1:3

+    printf('\n')

+    for j=1:3

+        printf(' %g\t',I(i,j))

+    end

+    for j=1:3

+        printf('%g\t',A(j,i))

+    end

+end

+printf('\n\n\n\n\n xi\tyi\tzi\tR1\tR2\tR3\n---------------------------------------------\n')

+I1=[0,0,0;0,0,1;0,1,0;1,0,0]

+for i=1:4

+    for j=1:3

+        l=0;

+        for k=1:i

+            l=l+I1(k,j)

+        end

+        I(i,j)=l

+    end

+end

+X=eye(1,6)-eye(1,6)

+for i=1:4

+    printf('\n')

+    for j=1:3

+        printf(' %g\t',I1(i,j))

+        X(j)=X(j)+I1(i,j)

+    end

+    for j=1:3

+        printf('%g\t',R(j,I(i,1),I(i,2),I(i,3)))

+        if i==4 then

+            X(j+3)=X(j+3)+R(j,I(i,1),I(i,2),I(i,3))

+        end

+    end

+end

+printf('\n---------------------------------------------\n')

+for i=1:6

+    printf(' %g\t',X(i))

+end

+printf('\n\n\nHence the solution is \n\t x = %g\n\t y = %g\n\t z = %g',X(1),X(2),X(3))
\ No newline at end of file
diff --git a/1670/CH3/EX3.22/3_22.sce b/1670/CH3/EX3.22/3_22.sce
new file mode 100755
index 000000000..a5e56ba09
--- /dev/null
+++ b/1670/CH3/EX3.22/3_22.sce
@@ -0,0 +1,48 @@
+//Example 3.22

+//Relaxation Method

+//Page no. 80

+clc;clear;close;

+

+A=[10,-2,1,-12;1,9,-1,-10;2,-1,11,-20]

+deff('y=R(i,x,y,z)','y=A(i,1)*x+A(i,2)*y+A(i,3)*z+A(i,4)')

+printf('dx\tdy\tdz\tdR1\tdR2\tR3\n---------------------------------------------')

+I=eye(3,3)

+for i=1:3

+    printf('\n')

+    for j=1:3

+        printf(' %g\t',I(i,j))

+    end

+    for j=1:3

+        printf('%g\t',A(j,i))

+    end

+end

+printf('\n\n\n\n\n xi\tyi\tzi\tR1\tR2\tR3\n---------------------------------------------\n')

+I1=[0,0,0;0,0,2;0,1,0;1,0,0;0,0,-0.3;0.2,0,0;0,0.2,0;0,-0.03,0;-0.016,0,0;0,0,0.009]

+for i=1:10

+    for j=1:3

+        l=0;

+        for k=1:i

+            l=l+I1(k,j)

+        end

+        I(i,j)=l

+    end

+end

+X=eye(1,6)-eye(1,6)

+for i=1:10

+    printf('\n')

+    for j=1:3

+        printf(' %g\t',I1(i,j))

+        X(j)=X(j)+I1(i,j)

+    end

+    for j=1:3

+        printf('%g\t',R(j,I(i,1),I(i,2),I(i,3)))

+        if i==10 then

+            X(j+3)=X(j+3)+R(j,I(i,1),I(i,2),I(i,3))

+        end

+    end

+end

+printf('\n---------------------------------------------\n')

+for i=1:6

+    printf(' %g\t',X(i))

+end

+printf('\n\n\nHence the solution is \n\t x = %g\n\t y = %g\n\t z = %g',X(1),X(2),X(3))
\ No newline at end of file
diff --git a/1670/CH3/EX3.23/3_23.sce b/1670/CH3/EX3.23/3_23.sce
new file mode 100755
index 000000000..38977f5d3
--- /dev/null
+++ b/1670/CH3/EX3.23/3_23.sce
@@ -0,0 +1,48 @@
+//Example 3.23

+//Relaxation Method

+//Page no. 81

+clc;clear;close;

+

+A=[10,-2,-3,-205;-2,10,-2,-154;-2,-1,10,-120]

+deff('y=R(i,x,y,z)','y=A(i,1)*x+A(i,2)*y+A(i,3)*z+A(i,4)')

+printf('dx\tdy\tdz\tdR1\tdR2\tdR3\n---------------------------------------------')

+I=eye(3,3)

+for i=1:3

+    printf('\n')

+    for j=1:3

+        printf(' %g\t',I(i,j))

+    end

+    for j=1:3

+        printf('%g\t',A(j,i))

+    end

+end

+printf('\n\n\n\n\n xi\tyi\tzi\tR1\tR2\tR3\n---------------------------------------------\n')

+I1=[0,0,0;20,0,0;0,19,0;0,0,18;10,0,0;0,6,0;0,0,2;2,0,0;0,0,1;0,1,0]

+for i=1:10

+    for j=1:3

+        l=0;

+        for k=1:i

+            l=l+I1(k,j)

+        end

+        I(i,j)=l

+    end

+end

+X=eye(1,6)-eye(1,6)

+for i=1:10

+    printf('\n')

+    for j=1:3

+        printf(' %g\t',I1(i,j))

+        X(j)=X(j)+I1(i,j)

+    end

+    for j=1:3

+        printf('%g\t',R(j,I(i,1),I(i,2),I(i,3)))

+        if i==10 then

+            X(j+3)=X(j+3)+R(j,I(i,1),I(i,2),I(i,3))

+        end

+    end

+end

+printf('\n---------------------------------------------\n')

+for i=1:6

+    printf(' %g\t',X(i))

+end

+printf('\n\n\nHence the solution is \n\t x = %g\n\t y = %g\n\t z = %g',X(1),X(2),X(3))
\ No newline at end of file
diff --git a/1670/CH3/EX3.3/3_3.sce b/1670/CH3/EX3.3/3_3.sce
new file mode 100755
index 000000000..28ee908ff
--- /dev/null
+++ b/1670/CH3/EX3.3/3_3.sce
@@ -0,0 +1,45 @@
+//Example 3.3

+//Gaussian Elimination Method

+//Page no. 54

+clc;clear;close;

+

+A=[10,-7,3,5,6;-6,8,-1,-4,5;3,1,4,11,2;5,-9,-2,4,7];           //augmented matrix

+disp(A,'Augmented Matrix=')

+C=A;

+//triangularization

+for i=1:4

+    for j=1:5

+        if i==1 then

+            B(i,j)=A(i,j)

+        elseif i==2

+            B(i,j)=A(i,j)-A(i,1)*A(i-1,j)/A(1,1)

+            B(i+1,j)=A(i+1,j)-A(i+1,1)*A(i-1,j)/A(1,1)

+            B(i+2,j)=A(i+2,j)-A(i+2,1)*A(i-1,j)/A(1,1)

+        elseif i==3

+            if j==1 then

+                C=B

+            else

+                B(i,j)=B(i,j)-C(i,2)*B(i-1,j)/B(2,2)

+                B(i+1,j)=C(i+1,j)-C(i+1,2)*C(i-1,j)/C(2,2)

+            end

+        else

+            if j==1 then

+                C=B

+            end

+                B(i,j)=B(i,j)-C(i,3)*B(i-1,j)/B(3,3)

+        end

+    end

+end

+

+disp(B,'Triangulated Matrix=')

+//back substitution

+x(4)=B(4,5)/B(4,4);

+printf('\nx(4) = %.0f\n',x(4))

+for i=3:-1:1

+    k=0

+    for j=i+1:4

+       k=k+B(i,j)*x(j)

+    end

+    x(i)=(1/B(i,i))*(B(i,5)-k)

+     printf('\nx(%i) = %.0f\n',i,x(i))

+end

diff --git a/1670/CH3/EX3.4/3_4.sce b/1670/CH3/EX3.4/3_4.sce
new file mode 100755
index 000000000..dda8574e1
--- /dev/null
+++ b/1670/CH3/EX3.4/3_4.sce
@@ -0,0 +1,36 @@
+//Example 3.4

+//Gaussian Elimination Method

+//Page no. 55

+clc;clear;close;

+

+A=[2,1,1,10;3,2,3,18;1,4,9,16];           //augmented matrix

+disp(A,'Augmented Matrix=')

+//triangularization

+for i=1:3

+    for j=1:4

+        if i==1 then

+            B(i,j)=A(i,j)

+        elseif i==2

+            B(i,j)=A(i,j)-A(i,1)*A(i-1,j)/A(1,1)

+            B(i+1,j)=A(i+1,j)-A(i+1,1)*A(i-1,j)/A(1,1)

+        elseif i==3

+            if j==1 then

+                A=B

+            end

+            B(i,j)=B(i,j)-A(i,2)*B(i-1,j)/B(2,2)

+        end

+    end

+end

+

+disp(B,'Triangulated Matrix=')

+//back substitution

+x(3)=B(3,4)/B(3,3);

+printf('\nx(3)= %i\n',x(3))

+for i=2:-1:1

+    k=0

+    for j=i+1:3

+       k=k+B(i,j)*x(j)

+    end

+    x(i)=(1/B(i,i))*(B(i,4)-k)

+     printf('\nx(%i)= %i\n',i,x(i))

+end

diff --git a/1670/CH3/EX3.5/3_5.sce b/1670/CH3/EX3.5/3_5.sce
new file mode 100755
index 000000000..bb3d8ff98
--- /dev/null
+++ b/1670/CH3/EX3.5/3_5.sce
@@ -0,0 +1,38 @@
+//Example 3.5

+//Gauss-Jordan Method

+//Page no. 57

+

+clc;clear;close;

+

+A=[1,2,1,8;2,3,4,20;4,3,2,16];     //augmented matrix

+

+for i=1:3

+    j=i

+    while (A(i,i)==0 & j<=3)

+        for k=1:4

+            B(1,k)=A(j+1,k)

+            A(j+1,k)=A(i,k)

+            A(i,k)=B(1,k)

+        end

+        disp(A)

+        j=j+1

+    end

+    for k=4:-1:i

+        A(i,k)=A(i,k)/A(i,i)

+    end

+    disp(A)

+    for k=1:3

+        if(k~=i) then

+           l=A(k,i)/A(i,i)

+           for m=i:4

+               A(k,m)=A(k,m)-l*A(i,m)

+           end

+        end

+       

+    end

+    disp(A)

+end

+

+for i=1:3

+    printf('\nx(%i) = %g\n',i,A(i,4))

+end
\ No newline at end of file
diff --git a/1670/CH3/EX3.6/3_6.sce b/1670/CH3/EX3.6/3_6.sce
new file mode 100755
index 000000000..0c16f5324
--- /dev/null
+++ b/1670/CH3/EX3.6/3_6.sce
@@ -0,0 +1,38 @@
+//Example 3.6

+//Gauss-Jordan Method

+//Page no. 57

+

+clc;clear;close;

+

+A=[10,1,1,12;1,10,1,12;1,1,10,12];     //augmented matrix

+

+for i=1:3

+    j=i

+    while (A(i,i)==0 & j<=3)

+        for k=1:4

+            B(1,k)=A(j+1,k)

+            A(j+1,k)=A(i,k)

+            A(i,k)=B(1,k)

+        end

+        disp(A)

+        j=j+1

+    end

+    for k=4:-1:i

+        A(i,k)=A(i,k)/A(i,i)

+    end

+    disp(A)

+    for k=1:3

+        if(k~=i) then

+           l=A(k,i)/A(i,i)

+           for m=i:4

+               A(k,m)=A(k,m)-l*A(i,m)

+           end

+        end

+       

+    end

+    disp(A)

+end

+

+for i=1:3

+    printf('\nx(%i) = %g\n',i,A(i,4))

+end
\ No newline at end of file
diff --git a/1670/CH3/EX3.7/3_7.sce b/1670/CH3/EX3.7/3_7.sce
new file mode 100755
index 000000000..299562f0b
--- /dev/null
+++ b/1670/CH3/EX3.7/3_7.sce
@@ -0,0 +1,38 @@
+//Example 3.7

+//Gauss-Jordan Method

+//Page no. 58

+

+clc;clear;close;

+

+A=[1,1,1,9;2,-3,4,13;3,4,5,40];     //augmented matrix

+

+for i=1:3

+    j=i

+    while (A(i,i)==0 & j<=3)

+        for k=1:4

+            B(1,k)=A(j+1,k)

+            A(j+1,k)=A(i,k)

+            A(i,k)=B(1,k)

+        end

+        disp(A)

+        j=j+1

+    end

+    for k=4:-1:i

+        A(i,k)=A(i,k)/A(i,i)

+    end

+    disp(A)

+    for k=1:3

+        if(k~=i) then

+           l=A(k,i)/A(i,i)

+           for m=i:4

+               A(k,m)=A(k,m)-l*A(i,m)

+           end

+        end

+       

+    end

+    disp(A)

+end

+

+for i=1:3

+    printf('\nx(%i) = %g\n',i,A(i,4))

+end
\ No newline at end of file
diff --git a/1670/CH3/EX3.8/3_8.sce b/1670/CH3/EX3.8/3_8.sce
new file mode 100755
index 000000000..e6af734ef
--- /dev/null
+++ b/1670/CH3/EX3.8/3_8.sce
@@ -0,0 +1,56 @@
+//Example 3.8

+//Triangularization Method

+//Page no. 60

+clc;clear;close;

+

+A=[1,2,3;2,5,2;3,1,5];

+B=[14;18;20];

+printf('A can be factorizaed as follows:\n')

+printf('\tL\t\t  *\t\tU\t\t  =\t\tA')

+U(2,1)=0;U(3,1)=0;U(3,2)=0;

+L(1,2)=0;L(1,3)=0;L(2,3)=0;

+for i=1:3

+    L(i,i)=1

+end

+for i=1:3

+    U(1,i)=A(1,i)

+end

+L(2,1)=A(1,2)/U(1,1);

+for i=2:3

+    U(2,i)=A(2,i)-U(1,i)*L(2,1);

+end

+L(3,1)=A(1,3)/U(1,1);

+L(3,2)=(A(3,2)-U(1,2)*L(3,1))/U(2,2);

+U(3,3)=A(3,3)-U(1,3)*L(3,1)-U(2,3)*L(3,2);

+printf('\n')

+for i=1:3

+    for j=1:3

+        printf('%.2f\t',L(i,j))

+    end

+    

+    if(i==2)

+        printf('  *     ')

+    else

+        printf('\t')

+    end

+    

+    for j=1:3

+        printf('%.2f\t',U(i,j))

+    end

+    if(i==2)

+        printf('  =     ')

+    else

+        printf('\t')

+    end

+    for j=1:3

+        printf('%.2f\t',A(i,j))

+    end

+    printf('\n')

+end

+printf('\nY=U*X')

+    Y=inv(L)*B

+    X=inv(U)*Y

+printf('\n\nX=')

+for i=1:3

+    printf('\n   %i',X(i,1))

+end
\ No newline at end of file
diff --git a/1670/CH3/EX3.9/3_9.sce b/1670/CH3/EX3.9/3_9.sce
new file mode 100755
index 000000000..22e6c7d3c
--- /dev/null
+++ b/1670/CH3/EX3.9/3_9.sce
@@ -0,0 +1,48 @@
+//Example 3.9

+//Triangularization Method

+//Page no. 61

+clc;clear;close;

+

+A=[1,2,3;2,5,2;3,1,5];

+B=[14;18;20];

+printf('A =\n')

+

+U(2,1)=0;U(3,1)=0;U(3,2)=0;

+L(1,2)=0;L(1,3)=0;L(2,3)=0;

+for i=1:3

+    L(i,i)=1

+end

+for i=1:3

+    U(1,i)=A(1,i)

+end

+L(2,1)=A(1,2)/U(1,1);

+for i=2:3

+    U(2,i)=A(2,i)-U(1,i)*L(2,1);

+end

+L(3,1)=A(1,3)/U(1,1);

+L(3,2)=(A(3,2)-U(1,2)*L(3,1))/U(2,2);

+U(3,3)=A(3,3)-U(1,3)*L(3,1)-U(2,3)*L(3,2);

+printf('\n')

+for i=1:3

+    for j=1:3

+        printf('%.2f\t',L(i,j))

+    end

+    

+    if(i==2)

+        printf('  *     ')

+    else

+        printf('\t')

+    end

+    

+    for j=1:3

+        printf('%.2f\t',U(i,j))

+    end

+    printf('\n')

+end

+

+    Y=inv(L)*B

+    X=inv(U)*Y

+printf('\n\nX=')

+for i=1:3

+    printf('\n   %i',X(i,1))

+end
\ No newline at end of file