How to Transform vectors?

Question

vector(-9,2) is transformed using the matrix A= -4 1

-1 2

What is the resulting vector?

Answer 1

An (x,y) point can be represented in matrix form as |x y|

Then vector(-9,2) is transformed using the matrix A= |-4 1|

| 1 2|

|-9 2| |-4 -1| = |36+2 9+4| = |38 13| Using matrix multiplication rules.

| 1 2|

Answer 2

| -4 1 | | -9 |

| -1 2 | | 2 |

<(-4)(-9) + (1)(2), (-1)(-9)+ (2)(2).

<36 + 2, 9 + 4>

<38, 13>