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Let \(u\) and \(v\) be three-dimensional vectors such that the length of \(u\) is \(2\), the length of \(v\) is \(4\), and the angle between \(u\) and \(v\) when placed tail to tail is \(120^{\circ}\).

 

Let \(\mathbf{A}\) be a \(3\times 3\) matrix such that 

\(\mathbf{row}_1(\mathbf{A}) = \mathbf{u}, \mathbf{row}_2(\mathbf{A}) = \mathbf{v}, \mathbf{row}_3(\mathbf{A}) =3\mathbf{u} + 2\mathbf{v}.\)

 

Then what are \(\mathbf{Au}\) and \(\mathbf{Av}\) in that order? (Your answers should be numerical.)

 Oct 24, 2021
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$\mathbf{A} \mathbf{u} = \begin{pmatrix} 4 \\ -4 \\ 8 \end{pmatrix}$

 

$\mathbf{A} \mathbf{v} = \begin{pmatrix} -8 \\ 12 \\ -16 \end{pmatrix}$

 Oct 24, 2021

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