# Math Help - Linear Transformations

1. ## Linear Transformations

I looked everywhere in the book for answer for this kind of question and they don't have it.

all they have is the easy case where T[1 0] and T[0 1]

it's in the attachment below

2. Originally Posted by akhayoon
I looked everywhere in the book for answer for this kind of question and they don't have it.

all they have is the easy case where T[1 0] and T[0 1]

it's in the attachment below
Well, solve
$\left ( \begin{matrix} a & b \\ c & d \end{matrix} \right ) \left ( \begin{matrix} 1 \\ 1 \end{matrix} \right ) = \left ( \begin{matrix} 3 \\ -2 \end{matrix} \right )$

and

$\left ( \begin{matrix} a & b \\ c & d \end{matrix} \right ) \left ( \begin{matrix} 1 \\ -1 \end{matrix} \right ) = \left ( \begin{matrix} 1 \\ 5 \end{matrix} \right )$

for a, b, c, and d.

After you get that, see if
$Tx + Ty = T(x + y)$
where x and y are arbitrary column vectors.

-Dan