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.)
