Assume that T is a linear transformation. Find the standard matrix of T. T: R^3 right arrow R^2 , T(e 1) =(1,2), and T(e2 ) =( -4,6), and T(e 3 ) =(2, -6), where e 1, e2 , and e 3 are the columns of the 3 x 3 identity matrix. A= (Type an integer or decimal for each matrix element.)

Step-by-step explanation:

Given

Required

Find the standard matrix

The standard matrix (A) is given by

Where

becomes

The x on both sides cancel out; and, we're left with:

Recall that:

In matrix:

is represented as:

So:

Substitute the above expressions in

Hence, the standard of the matrix A is: