### Home > PC > Chapter 12 > Lesson 12.2.1 > Problem12-41

12-41.

A matrix $M$ takes $\left(1, 0\right)$ to $\left(2, 0\right)$ and $\left(0, 1\right)$ to $\left(0, 2\right)$.

1. Find $M$ explicitly.

$\left[ \begin{array} { l l } { 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right] M = \left[ \begin{array} { l l } { 2 } & { 0 } \\ { 0 } & { 2 } \end{array} \right]$

2. Describe what $M$ does to any point.

Any point $\left(a, b\right)$ multiplied by matrix $M$:

$\left( \begin{array} { l l } { a , b } & { b } \end{array} \right) \left[ \begin{array} { l l } { 2 } & { 0 } \\ { 0 } & { 2 } \end{array} \right] = ( 2 a , 2 b )$