initial commit / add all books

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diff --git a/60/CH4/EX4.1/ex_1.sce b/60/CH4/EX4.1/ex_1.sce
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+
+//Example (pg no.130)
+
+          A=[3 0 2;1 2 0;0 1 1]
+          B=[2 1;0 1;1 0]
+            A*B
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diff --git a/60/CH4/EX4.14/ex_14.sce b/60/CH4/EX4.14/ex_14.sce
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+//example(3.14)
+
+ c=[-3 1 0 1]
+ p3=poly(c,'y','coeff')
+ roots(p3)
+ 
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diff --git a/60/CH4/EX4.16/ex_16.sce b/60/CH4/EX4.16/ex_16.sce
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+//Example (pg no.186)
+
+
+//(1)
+         A=[1 4;2 3]
+         det(A)
+
+//(2)
+         A=[4 1;3 2]
+         det(A)
diff --git a/60/CH4/EX4.17/ex_17.sce b/60/CH4/EX4.17/ex_17.sce
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+//Example (pg no.186)
+
+        A=[3.1 4;3.2 3]
+        det(A)
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diff --git a/60/CH4/EX4.18/ex_18.sce b/60/CH4/EX4.18/ex_18.sce
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index 000000000..351e6c249
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+//Example (pg no.186)
+
+         A=[1 2;2 2]
+         B=[1 2;1 1]
+         det(A)+det(B)
+         C=[1 2; 3 3]
+         det(C)
+           //det(A)+det(B)=det(C)
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diff --git a/60/CH4/EX4.19/ex_19.sce b/60/CH4/EX4.19/ex_19.sce
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index 000000000..c9f25dad3
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+//Example(4.11) (pg no.191)
+
+          B=[1 2 0;2 1 0;0 0 -1]
+          lam = spec(B)
diff --git a/60/CH4/EX4.2/ex_2.sce b/60/CH4/EX4.2/ex_2.sce
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index 000000000..7c2843a63
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+//Example (pg no.130)
+
+
+       A=[2 1;1 3]
+       B=[2 1;0 1]
+       A*B
+       B*A
+//matrix multiplication is not commutative
+            //so A*B!=B*A
+
diff --git a/60/CH4/EX4.20/ex_20.sce b/60/CH4/EX4.20/ex_20.sce
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index 000000000..4b9dd2598
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+//Example(4.14) (pg no.201)
+
+
+B=[1 2 0;2 1 0;0 0 -1]
+lam = spec(B)
+norm(B)
+        //Each eigen value of the matrix must have absolute value
+        //      no bigger than the norm of that matrix 
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diff --git a/60/CH4/EX4.21/ex_21.sce b/60/CH4/EX4.21/ex_21.sce
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+//Example(4.15) (pgno 202)
+
+B=[1 2 0;2 1 0;0 0 -1]
+I=[1 0 0;0 1 0;0 0 1]
+         //here we are taking lamda=a
+         //det(B-a)*I=0 is characteristic equation to get lamda
+deff('[y]=p(a)','p(a)=det(B-a)*I')
+p(a)=0
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diff --git a/60/CH4/EX4.22/ex_22.sce b/60/CH4/EX4.22/ex_22.sce
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+//Example(4.16)(page no.203)
+
+A=[4 -1 -1 -1;-1 4 -1 -1;-1 -1 4 -1;-1 -1 -1 4]
+spec(A)
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diff --git a/60/CH4/EX4.3/ex_3.sci b/60/CH4/EX4.3/ex_3.sci
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+//Example (pg no.133)    
+
+       A=[1 1;0 1]
+       inv(A)
+       B=[1 0;1 1]
+       inv(B)
+       A*B
+       inv(A*B)
+       inv(A)*inv(B)
+                                       //inv(A*B)=inv(B)*inv(A)
+       inv(B)*inv(A)
+                                         //Hence inv(A)*inv(B) = inv(A)*inv(B)
+        I=eye(3,3)
+        C=(A*B)*(inv(A)*inv(B))
+                                        //C!=I 
+                                         //so, inv(A)*inv(B) cannot be the inverse of (A*B)
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diff --git a/60/CH4/EX4.4/ex_4.sce b/60/CH4/EX4.4/ex_4.sce
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+
+ //Example (pg no.136)
+ 
+ // x1 + 2(x2) = 3
+ //2(x1) + 4(x2) = 6
+ 
+        A=[1 2;2 4]
+            //coefficient matrix of above equations
+        b=[3 6]'
+        x=A\b
+     //for corresponding homogenous system
+             //  x1 + 2(x2) = 0
+            //2(x1) + 4(x2) = 0
+         A=[1 2;2 4]
+             //coefficient matrix of above equations
+        b=[0 0]'
+        x=A\b
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diff --git a/60/CH4/EX4.6/ex_6.sce b/60/CH4/EX4.6/ex_6.sce
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+//Example (pg no.140)
+
+         A=[1 2;2 4]
+         det(A)
+                        // Here A is a singular matrix i.e, det(A)=0
+                        //inv(A)=(adj(A))/det(A)
+                        //so A is not invertible
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diff --git a/60/CH4/EX4.7/ex_7.sce b/60/CH4/EX4.7/ex_7.sce
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+//Example (pg no.144)
+
+A = [1 2 3;4 5 6;7 8 9]
+[L,U,E] = lu(A)
+       // L is lower triangular matrix(mxn)
+       // U is upper triangular matrix(mxmin(m,n))
+      // E is permutation matrix(min(m,n)xn)
+A*E
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diff --git a/60/CH4/EX4.8/ex_8.sce b/60/CH4/EX4.8/ex_8.sce
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+//example 4.1 (pg 149)
+
+     //2x1 + 3x2 - x3 = 5
+    //-2x2 - x3 = -7
+   //-5x3 = -15
+
+A = [2 3 -1;0 -2 -1;0 0 -5]
+b = [5 -7 -15]'
+a=[A b]
+[nA,mA]=size(A)
+n=nA
+
+     //Backward substitution
+
+x(3) = a(n,n+1)/a(n,n);
+
+for i = n-1:-1:1
+	sumk=0;
+	for k=i+1:n
+		sumk=sumk+a(i,k)*x(k);
+	end
+	x(i)=(a(i,n+1)-sumk)/a(i,i); 
+end
+    disp(x)
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