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

 Nov 27, 2019

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