### Home > PC > Chapter 12 > Lesson 12.2.3 > Problem12-63

12-63.

If $l$ and $m$ are perpendicular lines, find a linear transformation $T$ such that $lT$ and $mT$ are not perpendicular.

Many linear transformations are possible. Make one up and try it.

$l =\langle t, 2t \rangle$

$m =\langle t, -\frac{1}{2}t \rangle$

$T = \left[ \begin{array} { l } { 1 } & { 2 } \\ { 3 } & { 4 } \end{array} \right]$

$lT =\langle 7t, 10t \rangle$

$m =\langle -\frac{1}{2}t, 0 \rangle$

What are the equations of these lines? Are they perpendicular?