Use the standard matrix for the linear transformation T to f

Use the standard matrix for the linear transformation T to find the image of the vector v. T(x, y) = (x + y, x - y, 3x, 3y), v = (7, -7) T(v) =

Solution

Let T(x,y) = (x+y , x-y , 3x , 3y)

Standard matrix = [ 1 1

1 -1

3 0

0 3 ]

Image of the vector =

[ 1 1

1 -1

3 0

0 3 ] * [7

-7]

= [ 7- 7

7+7

21 +0

0 -21 ]

= [ 0

14

21

-21 ]

is our answer/