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Matrix Operations. Matrix Equations/Inverses. Determinants. Other Junk. 100. 100. 100. 100. 200. 200. 200. 200. 300. 300. 300. 300. 400. 400. 400. 400. Row 1, Col 1. The 2x2 zero matrix. Find AB. 1,2. The 2x2 identity matrix. Find the inverse of the 2x2 identity matrix.

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Presentation Transcript
slide1

Matrix Operations

Matrix Equations/Inverses

Determinants

Other Junk

100

100

100

100

200

200

200

200

300

300

300

300

400

400

400

400

row 1 col 1
Row 1, Col 1

The 2x2 zero matrix.

Find AB.

slide3
1,2

The 2x2 identity matrix

Find the inverse of the 2x2

identity matrix.

slide4
1,3

2

Find the area of the triangle with vertices

A(-3,2), B(-1,4), C(-4,3)

slide5
1,4

B

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

slide6
2,1

Not enough information to tell

Suppose the product AB is a 4x4

matrix. We know that A has 4 rows.

How many rows does B have?

slide7
2,2

Solve the matrix equation.

X +

=

slide8
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=

slide9
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

slide10
3,1

Two softball teams submit equipment lists for the season:

Women: Men:

12 bats 15 bats

45 balls 38 balls

15 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.

slide11
3,2

C-1B-1A-1

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.

slide12
3,3

0

What is the determinant

of:

slide13
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

slide14
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)

slide15
4,2

Gabriel and Cosmo

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.

slide16
4,3

This is false. For instance, consider A and B both as 2x2 identity matrices to get a counterexample to the claim.

Prove or disprove

(with a counterexample):

For any matrices A and B,

det(A+B)=det(A)+det(B).

slide17
4,4

Graphing, Linear Combination/Elimination, Substitution, Cramer’s Rule, Calculator/RREF, Inverse Matrices

Name six methods you could use

to solve a system of two equations

in two variables.

(All six or nothing!)