## Math 116: Study Guide - Chapter 6

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.
4. Determine if each matrix is in row echelon form, reduced row echelon form, or neither.
5. Solve the system of linear equations using Gauss Jordan elimination
6. Solve the system of linear equations using Cramer's Rule
7. 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
8. Given two 2x2 matrices A and B, find: A + B, 2A, 3A-2B, AB, A2, |A|, and A-1.
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 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