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-rw-r--r--Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.1.1/Ex8.1_1.r14
-rw-r--r--Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.1.2/Ex8.1_2.r15
-rw-r--r--Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.2.1/Ex8.2_1.r15
-rw-r--r--Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.1/Ex8.3_1.r8
-rw-r--r--Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.3/Ex8.3_3.r11
-rw-r--r--Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.4/Ex8.3_4.r10
-rw-r--r--Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.5/Ex8.3_5.r10
-rw-r--r--Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.5.2/Ex8.5_2.r19
-rw-r--r--Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.6.2/Ex8.6_6.r6
9 files changed, 108 insertions, 0 deletions
diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.1.1/Ex8.1_1.r b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.1.1/Ex8.1_1.r
new file mode 100644
index 00000000..25d952f3
--- /dev/null
+++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.1.1/Ex8.1_1.r
@@ -0,0 +1,14 @@
+# Example : 1 Chapter : 8.1 Page No: 413
+# Find movements , tensions, elongations of spring
+K<-matrix(c(2,-1,0,-1,2,-1,0,-1,2),ncol=3)
+K1<-solve(K)
+f<-c(1,1,1)#since all mi=m
+u<-K1%*%f
+print("Movements are given by mg/c * u and u is")
+print(u)
+A<-matrix(c(1,-1,0,0,0,1,-1,0,0,0,1,-1),ncol=3)
+e<-A%*%u
+print("Elongations are given by mg/c * e and e is")
+print(e)
+print("Tensions are given by mg * e and e is")
+print(e) \ No newline at end of file
diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.1.2/Ex8.1_2.r b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.1.2/Ex8.1_2.r
new file mode 100644
index 00000000..5a83baa2
--- /dev/null
+++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.1.2/Ex8.1_2.r
@@ -0,0 +1,15 @@
+# Example : 2 Chapter : 8.1 Page No: 414
+# Find movements , tensions, elongations of spring
+K1<-matrix(c(2,-1,0,-1,2,-1,0,-1,1),ncol=3)
+K11<-solve(K1)
+f<-c(1,1,1)
+u<-K11%*%f
+print("Movements are given by mg/c * u and u is")
+print(u)
+A<-matrix(c(1,-1,0,0,1,-1,0,0,1),ncol=3)
+e<-A%*%u
+print("Elongations are given by mg/c * e and e is")
+print(e)
+y<-solve(t(A))%*%f
+print("Tensions are given by mg * y and y is")
+print(y) \ No newline at end of file
diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.2.1/Ex8.2_1.r b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.2.1/Ex8.2_1.r
new file mode 100644
index 00000000..d5687138
--- /dev/null
+++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.2.1/Ex8.2_1.r
@@ -0,0 +1,15 @@
+# Example : 1 Chapter : 8.2 Page No: 427
+# Find the currents
+A<-matrix(c(-1,-1,0,-1,0,0,1,0,-1,0,-1,0,0,1,1,0,0,-1,0,0,0,1,1,1),ncol=4)
+AT<-t(A)
+Laplacian_matrix<-AT%*%A
+Laplacian_matrix<-Laplacian_matrix[-4,-4]
+b<-c(1,0,0)
+x<-solve(Laplacian_matrix,b)
+x<-c(x,0)
+print("Voltages are given by S * ")
+print(x)
+print("S is source")
+y<--1*A%*%x
+print("Currents are given by S * ")
+print(y) \ No newline at end of file
diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.1/Ex8.3_1.r b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.1/Ex8.3_1.r
new file mode 100644
index 00000000..08516b62
--- /dev/null
+++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.1/Ex8.3_1.r
@@ -0,0 +1,8 @@
+# Example : 1 Chapter : 8.3 Page No: 432
+# Positive Markov matrix Application.
+A<-matrix(c(0.8,0.2,0.05,0.95),ncol=2)
+u0<-c(0.02,0.98)
+u1<-A%*%u0
+print(u1)
+u2<-A%*%u1
+print(u2) \ No newline at end of file
diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.3/Ex8.3_3.r b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.3/Ex8.3_3.r
new file mode 100644
index 00000000..e66f77d2
--- /dev/null
+++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.3/Ex8.3_3.r
@@ -0,0 +1,11 @@
+# Example : 3 Chapter : 8.3 Page No: 433
+# Markov matrix Application.
+A<-matrix(c(0,0.5,0.5,0.5,0,0.5,0.5,0.5,0),ncol=3)
+u0<-c(8,16,32)
+u1<-A%*%u0
+u2<-A%*%u1
+u3<-A%*%u2
+print("Populations in three groups in subsequent months")
+print(u1)
+print(u2)
+print(u3) \ No newline at end of file
diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.4/Ex8.3_4.r b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.4/Ex8.3_4.r
new file mode 100644
index 00000000..f94b4967
--- /dev/null
+++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.4/Ex8.3_4.r
@@ -0,0 +1,10 @@
+# Example : 4 Chapter : 8.3 Page No: 437
+# Linear Algebra in Economy
+A<-matrix(c(0.2,0.4,0.5,0.3,0.4,0.1,0.4,0.1,0.3),ncol=3)
+lambda<-eigen(A)$values
+print("Lambda max is ")
+print(lambda[1])
+I<-matrix(c(1,0,0,0,1,0,0,0,1),ncol=3)
+A1<-solve(I-A)
+print(A1)
+#The answers may vary due to rounding off values
diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.5/Ex8.3_5.r b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.5/Ex8.3_5.r
new file mode 100644
index 00000000..1858f801
--- /dev/null
+++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.3.5/Ex8.3_5.r
@@ -0,0 +1,10 @@
+# Example : 5 Chapter : 8.3 Page No: 437
+# Linear Algebra in Economy
+A<-matrix(c(0,1,4,0),ncol=2)
+lambda<-eigen(A)$values
+print("Lambda max is ")
+print(lambda[1])
+I<-matrix(c(1,0,0,1),ncol=2)
+A1<-solve(I-A)
+print(A1)
+#The answers may vary due to rounding off values
diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.5.2/Ex8.5_2.r b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.5.2/Ex8.5_2.r
new file mode 100644
index 00000000..634de0d9
--- /dev/null
+++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.5.2/Ex8.5_2.r
@@ -0,0 +1,19 @@
+#integrate is a function from package stats which is included in R by default
+#if not install package stats
+# Example : 2 Chapter : 8.5 Page No: 448
+# length of function sinx and sinx and cosx are orthogonal in function space
+f1<-function(x){
+ return (sin(x)*sin(x))
+}
+f2<-function(x){
+ return (sin(x)*cos(x))
+}
+print("Inner product of sinx and sinx is ")
+lsin2x<-integrate(f1,0,2*pi)
+print(lsin2x)
+print("Length of sinx is square root of above inner product")
+print(sqrt(lsin2x$value))
+print("Cos x and sinx are orthogonal in functional space because their inner product equals zero")
+lsinxcosx<-integrate(f2,0,2*pi)
+print(lsinxcosx)
+#The answer may slightly vary due to rounding off values \ No newline at end of file
diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.6.2/Ex8.6_6.r b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.6.2/Ex8.6_6.r
new file mode 100644
index 00000000..91c1dffb
--- /dev/null
+++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH8/EX8.6.2/Ex8.6_6.r
@@ -0,0 +1,6 @@
+# Example : 6 Chapter : 8.6 Page No: 457
+# Singualar Value Decomposition
+gradematrixA<-matrix(c(-6,0,4,2,2,4,0,-6,0,-6,2,4,4,2,-6,0),ncol=4)
+print("SVD of Grade matrix is")
+print(svd(gradematrixA))
+#The answers may vary due to rounding off values \ No newline at end of file