# Math 116 - Chapter 5 Study Guide

No calculators on this exam

1. Solve the system of equations by the method of substitution. One linear system, one non-linear system. Look at problems 5.1.15-28, 39-42, 49-50.
2. Find the system of linear equations that has the given solution. There is more than one possible solution. One part has an ordered pair, the other part has an ordered triplet. Look at problems 5.2.53-56, 5.3.39-42.
3. Use back substitution to find the solution to the system of equations. Look at problems 5.3.5-10.
4. Solve the system of equations by the method of elimination. Look at problems 5.2.7-16, 21-32.
5. Determine the order of the matrix. Look at problems 5.4.1-6.
6. Write the system of linear equations as an augmented matrix. Do not solve the system. Look at problems 5.4.7-10.
7. Determine if each matrix is in row echelon form, reduced row echelon form, or neither. Four parts. Look at problems 5.4.23-26.
8. Write the solution to the system of linear equations that corresponds to the augmented matrix shown. Three parts. Look at problems 5.4.39-46.
9. Solve the 2×2 system of linear equations using Gauss Jordan elimination. Look at problems 5.4.47-48, 51-54
10. Solve the 2×2 system of linear equations using Cramer's Rule. Look at problems 5.8.15-20.
11. Solve the matrix equations for X. Two 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. Look at problems 5.5.23-26, but you won't be given the actual matrices, just solve the equation.
12. Multiply two matrices together. Look at problems 5.5.27-34.
13. Given two 2×2 matrices A and B, be able to add the matrices, multiply by a scalar, multiply two matrices, square a matrix, find the determinant, find the transpose, and find the inverse. Look at problems 5.5.5-12, 35-30; 5.6.33-36.
14. Use a determinant to find the equation of a line passing through the given points. The model is given.
15. Solve a 3×3 system linear equations using any algebraic method, but show work.

## Notes:

• Where you are instructed to use a particular method of solving the system of equations, be sure you use that method.
• There are no calculators allowed on this exam. All of the problems have been designed with reasonably nice answers and small numbers to make the calculations easy to do by hand.
• There is a take home exam for this chapter worth 34 points. It is due the day of the exam.
• Each person has two encrypted messages to decode. It will be much easier to use Excel to do this than to use your calculator. Here are instructions for decrypting the message with Excel.

## Point values for each question

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Total 8 4 3 4 1 1 4 6 4 4 4 3 12 3 5 66