# Math 116 - Chapter 5 & 6 Study Guide

1. Write the solution to the system of linear equations that corresponds to the augmented matrix shown. Three parts.
2. Multiply two matrices together.
3. Given two 2×2 matrices A and B, be able to add the matrices, multiply by a scalar, multiply two matrices, find the determinant, and find the inverse.
4. Evaluate a 3×3 determinant.
5. Solve the system of linear equations by the method of substitution.
6. Solve the system of linear equations by the method of elimination.
7. Solve the system of llinear equations using Gauss-Jordan elimination.
8. Solve the system of linear equations using Cramer's Rule.
9. Solve a 3×3 system linear equations using any algebraic method, but show work.
10. Solve the system of linear equations by graphing.
11. Solve the system of linear equations using matrix algebra and inverses. Since this will be done on the calculator, your work can consist of the matrices you enter into the calculator and the expression used to find the solution. Look at problems 5.6.45-50.
12. 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.
13. Use back substitution to find the solution to the system of equations. Look at problems 5.3.5-10.
14. 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.
15. Write the first five terms of the sequence.
16. Find the most apparent pattern for the general term of the sequence.
17. Simplify the expression involving the ratio of the factorials:
18. Find the sum, given in summation notation.
19. Given the first term and common difference, write the first five terms of an arithmetic sequence.
20. Given the first term and common difference, find a specific term in an arithmetic sequence.
21. Given the first term and last term of an arithmetic sequence, find the sum of the terms of the sequence.
22. Given the first term and common ratio, write the first five terms of the geometric sequence.
23. Given the first term and common ratio, find a specific term of a geometric sequence.
24. Given the first term and common ratio, find the sum of the first n terms of a geometric series.
25. Given an infinite geometric series in summation form, find the sum.

## Notes

• The first nine problems on the exam must be worked without a calculator. Once you have completed that part of the exam, turn it in and pick up the second part. You may use a calculator on the second part.
• There is a take home exam for this exam worth 25 points. It is due the day of the exam.
• Show work on the exam even if the calculator will do the problem for you. For questions 5-8 and 10-11, I need to see enough work to verify that you are using the indicated method. Make sure you use the indicated method, even if you can do it another way.
• You may bring in a notecard with these formulas on them.
• Arithmetic Sequences / Series: Common Difference, General Term, Sum of the first n terms (two formulas)
• Geometric Sequences / Series: Common Ratio, General Term, Sum of the first n terms, Sum of an infinite series
• Your notecard may not have examples on them. You may use both sides of a notecard or one side of an 8.5"×11" sheet of paper. The notecard must be handwritten and an original copy (make your own notecard). Place your name on the card. Cards will be looked at before the exam and collected with the test.
• The notecard can be used on the second part of the exam (the formulas aren't needed on the first part).

## Point values per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Total 3 4 10 3 5 5 5 5 5 5 5 5 3 4 3 3 3 3 3 3 3 3 3 3 3 100