## Math 116: Study Guide - Chapter 6

- Determine the order of the matrix
- Write the system of linear equations as an augmented matrix. Do not solve the system
- Solve the system of linear equations using Gauss Jordan elimination
- Solve the system of linear equations using Cramer's Rule
- Given two 2x2 matrices A and B, find: A + B, 3A, AB, A squared, A inverse, the determinant
of A. Also evaluate a function, f(A).
- Use a determinant to find the equation of a line passing through the given points. The model
is given.
- True or False - 5 parts. You should definitely know about commutativity and division of both
scalars and matrices.
- Some statements are given. You must decide if performing those operations will return an
row-equivalent matrix. Four parts.
- Solve the matrix equations for X. Three parts. Know that when you factor a scalar out of a
matrix, you need to multiply the scalar by I: example AX-5X = (A-5I)X, not (A-5)X
- Multiply two matrices together.
- Solve a 3x3 system linear equations using Gauss Jordan Elimination.

### Notes

- NO CALCULATORS on the in-class portion.
- The in-class portion is worth 60 points.
- There is a take-home portion designed to be used done with the calculator.
- The take-home portion is worth 40 points and will be due the day after the in-class exam.
- Show work where necessary. Parts of problem 5 are so simple that you could do the work in
your head.
- None of the problems are directly from the text.
- Make sure you use the proper technique (Gauss-Jordan or Cramer's Rule). You will miss half
the points if you use the wrong technique. Make sure you use Gauss-Jordan and not just
Gaussian reduction with back-substitution.
- On the problems that say use Gauss-Jordan reduction, you do not have to pivoting, you can
use the row operations of the textbook, but I encourage the use of pivoting.

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
Tot |

Pts |
3 |
3 |
6 |
6 |
14 |
3 |
5 |
4 |
6 |
4 |
6 |
60 |