2. 100 200 400 300 400 Matrix Operations Matrix Equations /Inverses Determinants Other Junk 300 200 400 200 100

3. Row 1, Col 1 Find AB. The 2x2 zero matrix.

4. 1,2 Find the inverse of the 2x2 identity matrix. The 2x2 identity matrix

5. 1,3 Find the area of the triangle with vertices A(-3,2), B(-1,4), C(-4,3) 2

6. 1,4 TRIVIA Where does the word "cryptography" come from? (A) Latin words meaning "hidden writing" (B) Greek words meaning "hidden writing” (C) Latin words meaning "cryptic writing" (D) Greek words meaning "cryptic writing B

7. 2,1 Suppose the product AB is a 4x4 matrix. We know that A has 4 rows. How many rows does B have? Not enough information to tell

8. 2,2 X += Solve the matrix equation.

9. 2,3 det(AB)=det(A)*det(B) Consider the matrices below. How is det(AB) related to det(A) and det(B)? A=B=

10. 2,4 (20, -1, -12, -8) Write a matrix equation and solve with your graphing calculator. w+6x+3y-3z=2 2w+7x+y+2z=5 w+5x+3y-3z=3 -6x-2y+3z=6

11. 3,1 Two softball teams submit equipment lists for the season: Women:Men: 12 bats15 bats 45 balls38 balls 15 uniforms17 uniforms Each bat costs $21, each ball costs $4, and each uniform costs $30. Let A be your equipment matrix and B be your cost matrix. Find the product AB to show the matrix representing the total cost for each team.

12. 3,2 DAILY DOUBLE Find a formula for (ABC) -1 similar to the one we found in class for (AB) -1. SHOW that your formula holds in general. C -1 B -1 A -1

13. 3,3 What is the determinant of: 0

14. 3,4 If you are using Cramer’s Rule to solve the following system for z, write the matrix which we take the determinant of which goes in the numerator: ax+by+cz=j dx+ey+fz=k gx+hy+iz=l

15. 4,1 All 3 of these are true The transpose of a matrix A is the matrix formed by interchanging the rows and the columns of A. How many of the following are true (0, 1, 2, or 3)? Name the true properties. A) B) C)

16. 4,2 TRIVIA What was Cramer’s first name (the math one!)? What was Kramer’s first name (the Seinfeld one!)? Must know BOTH for the points. Gabriel and Cosmo

17. 4,3 Prove or disprove (with a counterexample): For any matrices A and B, det(A+B)=det(A)+det(B). This is false. For instance, consider A and B both as 2x2 identity matrices to get a counterexample to the claim.

18. 4,4 Name six methods you could use to solve a system of two equations in two variables. (All six or nothing!) Graphing, Linear Combination/Elimination, Substitution, Cramer’s Rule, Calculator/RREF, Inverse Matrices