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# I will really appreciate any help.

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I will really appreciate any help.

Let $$\mathbf{A}, \mathbf{B}, \mathbf{C}, \mathbf{D}$$ be the following matrices:

\begin{align*} &\mathbf{A} = \begin{pmatrix} 0 & 0 \\ 0& 0 \end{pmatrix},\\ &\mathbf{B} = \begin{pmatrix} -1 & 0 \\ 0 & -1\end{pmatrix}, \\ &\mathbf{C} = \begin{pmatrix} 1/2 & 1/2 \\ 1/2 & 1/2\end{pmatrix}, \\ &\mathbf{D} = \begin{pmatrix} 0 & -1 \\ -1 & 0 \end{pmatrix}. \end{align*}

Also, consider the following functions:

\begin{align*} &\text{Reflection across a line with direction vector \begin{pmatrix}1\\-1 \end{pmatrix}},\\ &\text{The function that sends every vector to the zero vector}, \phantom{\begin{pmatrix}1\\-1 \end{pmatrix}}\\ &\text{The function that sends every vector to its negative},\phantom{\begin{pmatrix}1\\-1 \end{pmatrix}}\\ &\text{Projection onto \begin{pmatrix}1\\1 \end{pmatrix}}. \end{align*}

How do we order the list

$$\mathbf{A}, \mathbf{B}, \mathbf{C}, \mathbf{D}$$

to match the order of the functions above?

I am having a hard time understanding problem such as these.

Thank you in advance for any help

Jul 20, 2022