# Math Help - Linear transformation

1. ## Linear transformation

Hello MHF,

Consider the linear transformation
$T \left(\left[\begin{array}{cc}x_{1}\\x_{2}\end{array}\right]\right)=\left[\begin{array}{cc}3x_{1}+4x_{2}\\2x_{2}\end{array}\ right]$

(i) What is the standard matrix associated with this transformation.
(ii) Consider the image of the unit disk under the transformation $T$. What is the area of this image?

So I think that the standard matrix is just $A = \left[\begin{array}{cc}3&4\\0&2\end{array}\right]$, but I am not sure what to do for part 2 of this question..

2. Originally Posted by Robb
Hello MHF,

Consider the linear transformation
$T \left(\left[\begin{array}{cc}x_{1}\\x_{2}\end{array}\right]\right)=\left[\begin{array}{cc}3x_{1}+4x_{2}\\2x_{2}\end{array}\ right]$

(i) What is the standard matrix associated with this transformation.
(ii) Consider the image of the unit disk under the transformation $T$. What is the area of this image?

So I think that the standard matrix is just $A = \left[\begin{array}{cc}3&4\\0&2\end{array}\right]$, but I am not sure what to do for part 2 of this question..
your answer to (i) is correct and for (ii) the answer is $6 \pi=|\det A| \times (\text{area of the unit circle}).$