# Study Guide - Chapter 8

## In-Class Portion - 70 points

1. Know the three elementary row operations. Be able to list them.
2. Know the four requirements of being in reduced row-echelon form. Be able to list them.
3. You are given two matrices, X which is an axb matrix and Y which is a cxd matrix. Know the relationships that must exist between a, b, c, and d in order to be able to add X and Y, multiple X and Y, find the determinant of X, find the inverse of X. Also know what the determinant must be (or not be) in order for an inverse to exist. Four parts.
4. True or False, three parts. Properties of Matrix multiplication. English sentences given here: Example: "Matrix multiplication is associative".
5. Given two 2x2 matrices A and B. Find: A+B, Det A, AB, A inverse, 3A-2B, B squared. Given a function f, evaluate f(A). Look at problems 33 - 36 in section 8.2 for the last part.
6. Solve two matrix equations for X. Examples: AX=B, AX + B = CX + D
7. Solve two 3x3 systems of linear equations using Gauss-Jordan elimination. Gauss-Jordan elimination must be used. Pivoting is optional but encouraged. One of the systems is very easy (lot's of zero's).
8. Find the inverse of a 3x3 matrix.
9. Evaluate a 4x4 determinant (lots of zeros)
10. Know the effect each of the three elementary row operations has on a determinant. See table at bottom of page 522.
11. Four parts. Be able to simply some algebraic expressions involving matrices. In particular, look at prage 495, steps involved in solving AX=B on page 505, and a binomial squared (Warning! Matrix Multiplication is NOT commutative).

## Take home portion - 30 points

Due: Day of regular exam

1. 8.1.64
2. 8.2.44
3. 8.4.28 - Give your answer as a 3x3 matrix with each element replaced by its cofactor. Then go ahead and find the determinant.
4. 8.4.28 - Find the inverse of the matrix by dividing the adjoint of the matrix by the determinant. The adjoint is the transpose of the matrix of cofactors (what you found in #3).
5. 8.5.50
6. 8.6.22
7. 8.6.28
8. 8.6.40
9. 8.6.46
10. Discussion problem on page 497