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Question 1205105: Let P and R be the following matrices:
P projects vectors onto (2; 3). R reflects vectors across a line with direction (1; 4).
I don't know how to format matrices on here, so I will write the top row (horizontal) and the bottom row. These are both 2 x 2 matrices.
Calculate the matrix P[4 3][6 -2] - R [1 0][4 0].
Sorry if the matrices are unclear. In latex, you are calculating $\[\mathbf{P} \begin{pmatrix} 4 & 3 \\ 6 & -2 \end{pmatrix} - \mathbf{R} \begin{pmatrix} 1 & 0\\ 4 & 0\end{pmatrix}.\]$
Answer by kately(2)   (Show Source):
You can put this solution on YOUR website! From the fact that P projects vectors onto (2; 3), we can plug in vectors to get that P = {{4/13,6/13},{6/13,9/13}}.
From the fact that R reflects vectors across a line with direction (1; 4), we can plug in vectors to get that R = {{-15/17,8/17},{8/17,15/17}}.
Computing them with the values provided and subtracting, the final answer is
{{3,0},{2,0}}
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