14. Least Squares and Applications

Projection Onto Subspaces — Quiz

Test your understanding of projection onto subspaces with 5 practice questions.

Practice Questions

Question 1

Which statement best describes the projection of a vector onto a subspace $S$?

Question 2

If a vector $v$ already lies in a subspace $S$, what is its projection onto $S$?

Question 3

Project $v=(3,4)$ onto the $x$-axis.

Question 4

Find the projection of $v=(5,1)$ onto $\operatorname{span}\{(1,2)\}$.

Question 5

In least squares, what is true about the residual vector $r=b-A\hat{x}$?