describe referencing the linear transformation how the entri

describe, referencing the linear transformation, how the entries of matrix D were determined.

Let the transformation be R2-->R2 give the final tranformed vector of the form:

L=(ax+by, cx+dy)

For 1st case, putting X(1,4) where x=1, y=4;

We get

a+4b=3; ---equation 1

c+4d=6; ----equation 2

For second case X(2,5) we get

2a+5b=0; ---equation 3

2c+5d=9; -----equation 4

Therfore, from equation 1,3 solving simultaneously, we get

a= -5

b=2

Similiarly from equation 2,4 solving simultaneously we get

c=2;

d=1;

Therefore,now L =(2y-5x, 2x+y)

And hence clearly, the matrix D becomes:

D= [ -5 2 ]

[ 2 1 ]

Note: please mind the determinant sign, its not supported in my device. Sorry for the inconvenience caused. D is a 2x2 matrix.

While X = [ x y ]

Hence L=DX