0
$\begingroup$

Let $A = \begin{bmatrix} 0 & 9 \\ -1 & 6 \end{bmatrix}$ and $B=\{b_1,b_2\}$, where $b_1=\begin{bmatrix} 3 \\ 1 \end{bmatrix}, b_2 =\begin{bmatrix} 2 \\ 1 \end{bmatrix}$. Define $T: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ by $T(x)=Ax$. Find the matrix for $T$ relative to the basis $B$.

Is this the same as the change of coordinates from one matrix to another? If so I have the augmented matrix $\begin{bmatrix} 3 & 2 & 0 & 9\\ 1 & 1 & -1 & 6 \end{bmatrix}$ which yields $\begin{bmatrix} 1 & 0 & 2 & -3 \\ 0 & 1 & -3 & 9 \end{bmatrix}$, so then would the matrix be $\begin{bmatrix} 2 & -3 \\ -3 & 9 \end{bmatrix}$? This is also a little different from other problems I've done, as some given property usually has to be satisfied.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.