### Session Overview

We often want to find the line (or plane, or hyperplane) that best fits our data. This amounts to finding the best possible approximation to some unsolvable system of linear equations Ax = b. The algebra of finding these best fit solutions begins with the projection of a vector onto a subspace |

### Session Activities

#### Lecture Video and Summary

- Watch the video lecture Lecture 15: Projections onto Subspaces
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)

#### Suggested Reading

- Read Section 4.2 in the 4
^{th}or 5^{th}edition.

#### Problem Solving Video

- Watch the recitation video on Problem Solving: Projection onto Subspaces
- Recitation video transcript (PDF)

### Check Yourself

#### Problems and Solutions

Work the problems on your own and check your answers when you’re done.