# Precalculus Problems help ASAP!!!

Algebra

### Precalculus Problems help ASAP!!!

a) Let $$\mathbf{P}$$ be the $$2\times 2$$ matrix that projects vectors onto $$\mathbf{u} = \begin{pmatrix}2\\ -1 \end{pmatrix}$$. That is, $$\mathbf{P} \bold{v} = \operatorname{proj}_{\bold{u}} (\bold{v}) = \text{Projection of \mathbf{v} onto \mathbf{u}}.$$ Use the picture below (bottom attachment) to find $$\mathbf{P} \begin{pmatrix}2 \\ -1 \end{pmatrix} \text{ and } \mathbf{P} \begin{pmatrix}1 \\ 2 \end{pmatrix}$$ using the geometric meaning of the matrix. Enter the answers as columns in the order above.

b) Let $$\mathbf{P}$$ be the $$2\times 2$$ matrix that projects vectors onto $$\mathbf{u} = \begin{pmatrix}2\\ -1 \end{pmatrix}$$. That is, $$\mathbf{P} \bold{v} = \operatorname{proj}_{\bold{u}} (\bold{v}) = \text{Projection of \mathbf{v} onto \mathbf{u}}.$$ Use your answers from part (a) to figure out $$\mathbf{P}$$.

c) Use the matrix $$\mathbf{P}$$ you found in part (b) to figure out $$\mathbf{w}_1$$ and $$\mathbf{w}_2$$ in the diagram below (top attachment).
Attachments
Screen Shot 2019-10-13 at 8.15.44 PM.png (49.34 KiB) Viewed 288 times
Screen Shot 2019-10-13 at 7.28.52 PM.png (49.7 KiB) Viewed 288 times
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### Re: Precalculus Problems help ASAP!!!

Surely you know that the projection of any vector onto itself is just itself again?
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