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Diffstat (limited to 'Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1')
8 files changed, 79 insertions, 0 deletions
diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.1/Ex1_1.R b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.1/Ex1_1.R new file mode 100644 index 00000000..29aa56a6 --- /dev/null +++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.1/Ex1_1.R @@ -0,0 +1,6 @@ +#Example : 1 Chapter : 1 pageno : 1 +v<-matrix(c(1,1),2,1,TRUE) +w<-matrix(c(2,3),2,1,TRUE) +z<-v+w +z + diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.2.1/Ex1.2_1.R b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.2.1/Ex1.2_1.R new file mode 100644 index 00000000..ae9dccf2 --- /dev/null +++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.2.1/Ex1.2_1.R @@ -0,0 +1,14 @@ +#Example : 1 Chapter : 1.2 pgno:-11 + +#Computing the dotproduct of two vectors +dotproduct<-function(x,y){ + res<-0 + for(i in 1:length(x)){ + res<-res+x[i]*y[i] + } + res +} +v<-matrix(c(4,2),nrow=2,ncol=1,byrow = T) +w<-matrix(c(-1,2),nrow=2,ncol=1,byrow=T) +r<-dotproduct(v,w) +print(paste("Dot product of given vectors is",r)) diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.2.2/Ex1.2_2.R b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.2.2/Ex1.2_2.R new file mode 100644 index 00000000..1f023173 --- /dev/null +++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.2.2/Ex1.2_2.R @@ -0,0 +1,11 @@ +#Example : 2 Chapter : 1.2 pgno:-11 + +#Computing the dotproduct of two vectors +dotproduct<-function(x,y){ + dp<-sum(x*y) + return(dp) +} +weight<-matrix(c(4,2),nrow=2,ncol=1,byrow = T) +distance<-matrix(c(-1,2),nrow=2,ncol=1,byrow=T) +center_point<-dotproduct(weight,distance) +center_point
\ No newline at end of file diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.2.5/Ex1.2_5.R b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.2.5/Ex1.2_5.R new file mode 100644 index 00000000..d4e5a915 --- /dev/null +++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.2.5/Ex1.2_5.R @@ -0,0 +1,11 @@ +#Example : 5 Chapter : 1.2 pageno : 16 + +v<-c(2,1) +w<-c(1,2) +dotproduct<-sum(v*w) +magn_v<-sqrt(sum(v*v)) +magn_w<-sqrt(sum(w*w)) +cos_angle<-dotproduct/(magn_v*magn_w) +print(paste("Cosine of the angle between the given vectors is",cos_angle)) + + diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.2.a/Ex1_1.2A.R b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.2.a/Ex1_1.2A.R new file mode 100644 index 00000000..08e3cba5 --- /dev/null +++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.2.a/Ex1_1.2A.R @@ -0,0 +1,17 @@ +#Example : 1.2A Chapter : 1.2 Pageno : 17 +#Finds whether Schwartz and traingular inequality between the given vectors are satisfied +#Finds the Cosine of the angle between the given vectors +v<-c(3,4) +w<-c(4,3) +dp=sum(v*w) +magn_v=sqrt(sum(v*v)) +magn_w=sqrt(sum(w*w)) +if(dp<=magn_v*magn_w){ + print("Schwartz inequality is satisfied for the given vectors") +} +z=v+w +magn_sum=sqrt(sum(z*z)) +if(magn_sum<=magn_v+magn_w){ + print("Traingular inequality is satisfied for the given vectors") +} +print(paste("Cosine of the angle between the given vectors is ",dp/(magn_v*magn_w))) diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.2.b/Ex1_1.2B.R b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.2.b/Ex1_1.2B.R new file mode 100644 index 00000000..f6c244f7 --- /dev/null +++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.2.b/Ex1_1.2B.R @@ -0,0 +1,10 @@ +#Example : 1.2B Chapter : 1.2 Pageno:-18 +v<-c(3,4) +V<-v/sqrt(sum(v*v)) +print(paste("The Unit vector in the direction of the given vector is ", V[1]," ",V[2])) +u<-c(-4,3) +if(sum(u*v)==0){ + print("The vectors u and v are perpendicular to each other") +} +U = u/sqrt(sum(u*u)) +print(paste("The unit vector in the direction of u is",U[1]," ",U[2]))
\ No newline at end of file diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.2.c/Ex1_1.2C.R b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.2.c/Ex1_1.2C.R new file mode 100644 index 00000000..78b288fc --- /dev/null +++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.2.c/Ex1_1.2C.R @@ -0,0 +1,6 @@ +#Example : 1.2C Chapter : 1.2 Pageno : 18 +A<-matrix(c(2,-1,-1,2),ncol=2) +b<-c(1,0) +x<-solve(A,b) +print("The solution of system is :") +print(x)
\ No newline at end of file diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.3.a/Ex1_1.3A.R b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.3.a/Ex1_1.3A.R new file mode 100644 index 00000000..3b47cc4f --- /dev/null +++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH1/EX1.3.a/Ex1_1.3A.R @@ -0,0 +1,4 @@ +#Example : 1.3A Chapter : 1.3 Pageno : 27 +A=matrix(c(1,0,0,-1,1,0,1,-1,1),ncol=3,byrow=T) +A1=solve(A) # to find the inverse of the matrix +A1
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