What is the vector that results from transforming a⃗ by the transformation matrix?
a⃗= [ 5 ]
[−3 ]
B= [7 −6]
[3 −4]
What is the vector that results from transforming \(\vec{a}\) by the transformation matrix?
\(\vec{a} = \dbinom{5}{-3}\)
\(B = \begin{pmatrix} 7 & -6 \\ 3 & -4 \end{pmatrix}\)
My attempt:
\(\begin{array}{|rcll|} \hline \mathbf{\vec{a}B} &=& \mathbf{\dbinom{5}{-3}\begin{pmatrix} 7 & -6 \\ 3 & -4 \end{pmatrix}} \\\\ \vec{a}B &=& \dbinom{5*7+(-3)*3}{5*(-6)+(-3)*(-4)} \\\\ \mathbf{\vec{a}B} &=& \mathbf{\dbinom{26}{-18}} \\ \hline \end{array}\)