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Matrix Operations

Matrix Equations/Inverses

Determinants Other Junk

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Row 1, Col 1

Find AB.

The 2x2 zero matrix.

1,2

Find the inverse of the 2x2 identity matrix.

The 2x2 identity matrix

1,3

Find the area of the triangle with verticesA(-3,2), B(-1,4), C(-4,3)

2

1,4

TRIVIAWhere 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

2,1

Suppose the product AB is a 4x4matrix. We know that A has 4 rows.

How many rows does B have?

Not enough information to tell

2,2

X + =

Solve the matrix equation.

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=

2,4

(20, -1, -12, -8)

Write a matrix equation and

solve with your graphing calculator.

w+6x+3y-3z=22w+7x+y+2z=5w+5x+3y-3z=3-6x-2y+3z=6

3,1

Two softball teams submit equipment lists for the season:

Women: Men:12 bats 15 bats45 balls 38 balls15 uniforms 17 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.

3,2

DAILY DOUBLEFind a formula for (ABC)-1

similar to the one we found inclass for (AB)-1. SHOW that

your formula holds in general.

C-1B-1A-1

3,3

What is the determinantof:

0

3,4

If you are using Cramer’s Rule to solve the following system for z,

write the matrix which we takethe determinant of which goes in

the numerator:ax+by+cz=jdx+ey+fz=kgx+hy+iz=l

4,1

All 3 of these are true

The transpose of a matrix A isthe 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)

4,2

TRIVIAWhat 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

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.

4,4

Name six methods you could useto 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