# Study Guide - Chapter 8

## In-Class Portion - 70 points

- Know the three elementary row operations.
- Know the four requirements of being in reduced row-echelon form.
- Know when two matrices can be added.
- Know when two matrices can be multiplied.
- What requirement must be met for a matrix to have an inverse.
- True or False, three parts. Properties of Matrix multiplication. English sentences given here:
Example: "Matrix multiplication is associative".
- Given two 2x2 matrices A and B. Find: A+B, Det A, AB, A inverse, 3A-2B, B squared.
Given a function f, evaluate f(A).
- Solve two matrix equations for X.
- Solve two 3x3 systems of linear equations using Gauss-Jordan elimination. Gauss-Jordan
elimination must be used. Pivoting is optional but encouraged. One of the systems is very
easy (lot's of zero's).
- Find the inverse of a 3x3 matrix.
- Evaluate a 4x4 determinant (lots of zeros)
- True or False, 10 parts. Properties on matrices written in mathematical form. Most of these
involve order of operations (when is something commutative and when isn't it), but also look
for those properties given on Monday at the end of class and when A dot A inverse is I and
when it isn't.

## Take home portion - 30 points

**Due: Before Wednesday November 22 at 2:00 pm.**

- 8.6.10
- 8.6.20
- 8.6.26
- 8.6.32
- 8.6.36
- 8.6.38
- 8.6.42
- 8.6.46
- 8.6.50
- 8.6.54