13. Inner Products and Orthogonality

Working With Orthogonal Decompositions — Quiz

Test your understanding of working with orthogonal decompositions with 5 practice questions.

Practice Questions

Question 1

In an orthogonal decomposition of a vector $x$ relative to a subspace $W$, how is $x$ written?

Question 2

What is the orthogonal projection of $x=(3,4)$ onto the $x$-axis?

Question 3

If $x=u+v$ where $u\perp v$, what is $\|x\|^2$ equal to?

Question 4

Which vector lies in the orthogonal complement of the $x$-axis?

Question 5

In an orthogonal decomposition $x=p+r$ of a vector $x$ relative to a subspace $W$, which part is the projection onto $W$?