Precalculus Problems help ASAP!!!

Algebra

Precalculus Problems help ASAP!!!

Postby Guest » Sun Oct 13, 2019 8:17 pm

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

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

c) Use the matrix [tex]\mathbf{P}[/tex] you found in part (b) to figure out [tex]\mathbf{w}_1[/tex] and [tex]\mathbf{w}_2[/tex] in the diagram below (top attachment).
Attachments
Screen Shot 2019-10-13 at 8.15.44 PM.png
Screen Shot 2019-10-13 at 8.15.44 PM.png (49.34 KiB) Viewed 345 times
Screen Shot 2019-10-13 at 7.28.52 PM.png
Screen Shot 2019-10-13 at 7.28.52 PM.png (49.7 KiB) Viewed 345 times
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Re: Precalculus Problems help ASAP!!!

Postby Guest » Sun Oct 27, 2019 11:29 am

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