# Math 116 - Chapter 6 Study Guide

1. Determine the order of the matrix
2. Write the system of linear equations as an augmented matrix. Do not solve the system
3. Write the solution to the system of linear equations that corresponds to the augmented matrix shown. Three parts.
4. Determine if each matrix is in row echelon form, reduced row echelon form, or neither. Four parts.
5. Solve the 2×2 system of linear equations using Gauss Jordan elimination
6. Solve the 2×2 system of linear equations using Cramer's Rule
7. Solve the matrix equations for X. Four 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
8. Given two 2×2 matrices A and B, be able to add the matrices, multiply by a scalar, perform a linear combination of the two matrices (ex: 3A-2B), multiply two matrices, square a matrix, find the determinant, find the transpose, and find the inverse.
9. Use a determinant to find the equation of a line passing through the given points. The model is given.
10. Multiply two matrices together.
11. Solve an equation involving determinants for x.
12. Solve a 3×3 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 use pivoting, you can use the row operations of the textbook, but I encourage the use of pivoting.
• 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 Take Home Total 2 2 3 4 6 6 4 7 3 4 3 6 50 100