The vector $\begin{pmatrix} k \\

The vector $\begin{pmatrix} k \\ 2 \end{pmatrix}$ is orthogonal to the vector $\begin{pmatrix} 3 \\ 5 \end{pmatrix}$. Find $k$.I
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Latex:The vector $\begin{pmatrix} k \\ 2 \end{pmatrix}$ is orthogonal to the vector $\begin{pmatrix} 3 \\ 5 \end{pmatrix}$. Find
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2. asked by Zheng
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Compute the distance between the parallel lines given by\[\begin{pmatrix} 1 \\ 4 \end{pmatrix} + t \begin{pmatrix} 4 \\ 3
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Find the $2 \times 2$ matrix $\bold{A}$ such that\[\bold{A} \begin{pmatrix} 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 1 \\ 2
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Find the $2 \times 2$ matrix $\bold{A}$ such that\[\bold{A} \begin{pmatrix} 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 1 \\ 2
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Find the $2 \times 2$ matrix $\bold{A}$ such that\[\bold{A} \begin{pmatrix} 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 1 \\ 2
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For a vector $\bold{v}$, let $\bold{r}$ be the reflection of $\bold{v}$ over the line\[\bold{x} = t \begin{pmatrix} 2 \\ -1
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Consider the statistical set-up from the previous problem. In particular, recall that \mathbf{u}= \frac{1}{\sqrt{5}} (1,2)^ T
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A matrix P \in \mathbb {R}^{d \times d} is orthogonal (sometimes referred to as a rotation matrix ) if P P^ T = P^ T P = I_ d.
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Let $\bold{w} = \begin{pmatrix} 2 \\ -1 \end{pmatrix}$. There exists a $2 \times 2$ matrix $\bold{P}$ such that\[\text{proj}_{\b
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