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# What is the vector that results from transforming a⃗ by the transformation matrix?

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What is the vector that results from transforming a⃗ by the transformation matrix?

a⃗= [ 5 ]

[−3 ]

B= [7 −6]

[3 −4]

May 20, 2020

#1
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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:

$$\begin{array}{|rcll|} \hline \mathbf{\vec{a}B} &=& \mathbf{\dbinom{5}{-3}\begin{pmatrix} 7 & -6 \\ 3 & -4 \end{pmatrix}} \\\\ \vec{a}B &=& \dbinom{5*7+(-3)*3}{5*(-6)+(-3)*(-4)} \\\\ \mathbf{\vec{a}B} &=& \mathbf{\dbinom{26}{-18}} \\ \hline \end{array}$$

May 20, 2020
edited by heureka  May 20, 2020
#2
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this isnt how matrix multiplication works

Guest May 20, 2020