The question

a) Find the standard matrix $\displaystyle A_3$ of the transformation which projects $\displaystyle R^3$ onto the x - z plane.

b) Find the standard matrix $\displaystyle A_4$ of the transformation which projects the x - z plane in $\displaystyle R^3$ onto $\displaystyle R^2$.

c) Find the standard matrix $\displaystyle A_5$ of the transformation which 'embeds' $\displaystyle R^2$ as the x - z plane in $\displaystyle R^3$.

I'm not sure how to attempt these. Does it have something to do with $\displaystyle S=GG^T$? I can work out the first one in my head, but I'd like to know the algorithm for solving the questions.

Any assistance would be truly appreciated.