## 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
- Write the solution to the system of linear equations that corresponds to the augmented
matrix shown.
- Determine if each matrix is in row echelon form, reduced row echelon form, or neither.
- Solve the system of linear equations using Gauss Jordan elimination
- Solve the system of linear equations using Cramer's Rule
- 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
- Given two 2x2 matrices A and B, find: A + B, 2A, 3A-2B, AB, A
^{2}, |A|, and A^{-1}.
- Use a determinant to find the equation of a line passing through the given points. The
model is given.
- 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 50 points.
- There is a take-home portion designed to be used done with the calculator.
- The take-home portion is worth 50 points and will be due the day after the in-class exam.
- Show work where necessary. Parts of problem 8 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 |
1 |
2 |
2 |
3 |
5 |
5 |
6 |
14 |
3 |
4 |
5 |
50 |