Let T be the linear transformation defined by Tx1 x2 x3 x4

Let T be the linear transformation defined by T(x_1, x_2, x_3, x_4) = 4x_2 - 3x_3 + 6x_4. Find its associated matrix A. A = []. You have attempted this problem 0 times. You have unlimited attempts remaining.

Solution

To find the associated matrix A we need to find the image of the standard basis vectors.

T(1,0,0,0)=0

T(0,1,0,0)=4

T(0,0,1,0)=-3

T(0,0,0,1)=6

So the matrix A is

A=[0 4   -3   6]