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# help

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Let $\mathbf{P}$ be the matrix that projects onto $\mathbf{j}$: that is, we want $\mathbf{P}$ to satisfy $\mathbf{P} \mathbf{v} = \text{The projection of \mathbf{v} onto } \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}$for all vectors $\mathbf{v}$. Use the pictures below to calculate $\mathbf{P}\mathbf{i}, \mathbf{P} \mathbf{j}, \mathbf{P}\mathbf{k}$in that order, and enter them in as columns below.

Then calculate the matrix $\mathbf{P}$ that projects onto $\mathbf{j}$.

Jul 31, 2019

The matrix is $$\begin{pmatrix} -1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1 \end{pmatrix}$$.