# Instructor Guide for Week 7

Matrices and vectors are used to compactly describe systems with linear and time-invariant state updates. Impulses and impulse response are introduced. The deep concept here is linearity, and the benefits it brings, specifically being able to write the state and output response as a convolution sum.

We also begin to develop frequency domain concepts, using musical notes as a way to introduce the idea that signals can be given as sums of sinusoids.

### Problem session

- Bank balance examples in chapter 5.
- Bank balance problem (5.6) (requires Matlab).
- Matrix reviews from chapter 5.