I'm having some trouble with the following linear algebra question:
Projecting onto the $xz$-plane or the $yz$-plane can easily be performed through rotations. For instance, if you want to project onto the $xz$-plane,you need to rotate the $y$-axis to the $z$-axis (this is a rotation about the $x$-axis), then perform the projection, and rotate back. Write down the projection matrix which does just this.
So I'm pretty sure that the answer will be the product of $3$ matrices? Since we want to project on the $xz$-plane, we want to rotate about the $y$-axis around the $x$-axis to the $z$-axis.
I've tried for several hours, but I cannot come up with much. Any help is appreciated.
A projection matrix onto $xz$ plane is simply given by
$$P = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}$$
indeed for any $v=(a,b,c)$ we have
$$Pv=(a,0,c)$$