# If T :mathbb{R}^2 rightarrow mathbb{R}^2 is a linear transformation such that Tleft(begin{bmatrix}3 6 end{bmatrix}right)=begin{bmatrix}39 33 end{bmatrix} text{ and } Tleft(begin{bmatrix}6 -5 end{bmatrix}right)=begin{bmatrix}27 -53 end{bmatrix} then the standard matrix of T is A

If T :${\mathbb{R}}^{2}\to {\mathbb{R}}^{2}$ is a linear transformation such that

then the standard matrix of T is A
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Malena
Step 1
Given:

The standard matrix of T will be the product of two matrices.
Step 2
$T=\left(\begin{array}{cc}3& 39\\ 6& 33\end{array}\right)\left(\begin{array}{cc}6& 27\\ -5& -53\end{array}\right)$
$=\left(\begin{array}{cc}18-195& 81-2067\\ 36-165& 162-1749\end{array}\right)$
$=\left(\begin{array}{cc}-177& -1986\\ -129& -1587\end{array}\right)$
Therefore the standard matrix of T is $T=\left(\begin{array}{cc}-177& -1986\\ -129& -1587\end{array}\right)$
Jeffrey Jordon