### Home > PC > Chapter 12 > Lesson 12.1.1 > Problem12-11

12-11.

Notice that if $p = \langle 1 , -2 \rangle$ and $M = \left[ \begin{array} { c c } { 13 } & { - 30 } \\ { 5 } & { - 12 } \end{array} \right]$, then $pM = 3p = \langle3, −6\rangle$.

1. Find some other vector (or $1 × 2$ matrix) $q = \langle 10 , x \rangle$ such that $qM = 3q$.

$p M = \langle 1 ( 13 ) + ( - 2 ) ( 5 ) , \quad 1 ( - 30 ) + ( - 2 ) ( - 12 ) \rangle$

$q M = \langle 10 ( 13 ) + x ( 5 ) , \quad 10 ( - 30 ) = x ( - 12 ) \rangle$

$3 q = \langle 30,3 x \rangle$

2. Find a value for $x$ such that the vector $r = \langle 1 , x \rangle$ has the property$rM = −2r$.

$r M = \langle 1 ( 13 ) + x ( 5 ) , \quad 1 ( - 30 ) + x ( - 12 ) \rangle$