Matrices Precalculus

Presentation

•

Mathematics

•

9th - 12th Grade

•

Hard

Joseph Anderson

FREE Resource

10 Slides • 25 Questions

Matrices

Add, Subtract, Multiply, Determinant, Inverse

Intro to Matrices

rows

columns

Matrix A is a 2 x 3 matrix

Finding Terms in a Matrix

elements or entries

Multiple Choice

How many rows are in a 7 x 3 matrix?

Multiple Choice

How many columns are in a 5 x 4 matrix?

Multiple Choice

What are the dimensions of this matrix?

2 x 3

3 x 2

6 x 1

1 x 6

Multiple Choice

What is the value of element a₂₃?

-1

Multiple Choice

Element G₂₂ is

Add, Subtract, Scalar Multiplication

dimensions

Multiple Choice

Add.

No Sum Exists

Multiple Choice

What must be true in order to ADD two matrices?

They must be square.

The dimensions must be equal.

The determinant can't equal 0.

The column of the 1st must equal the row of the 2nd.

Multiple Choice

Find B-A

-3 1
7 -1

1 0
1 -4

4 0
-6 1

not possible because rows do not match columns

Multiple Choice

Multiply

20 15 -10
30 -5 0

-20 15 -10
30 -5 0

1 8 3
11 4 5

20 -15 10
-30 5 0

Multiple Choice

Multiply

25
25
5

-25
25
-5

-10
-10
-6

10
10
6

Matrix Equations

equal

3(5 x +3) = -36
15x + 9 = -36
15x = -45
X = -3

3(-4 + -y) = -27
-12 - 3y = -27
-3y = -15
Y = 5

Multiple Choice

What do w, x, y and z equal in this matrix subtraction?

w = 13, x = 4, y = 7, z = 23

w = 13, x = -4, y = 11, z = 23

w = 13, x = 4, y = 11, z = 23

w = 13, x = 4, y = 11, z = 17

Multiplication of Matrices

Multiplication Cont.

columns

rows

NOT

rows

columns

row

column

Multiple Choice

You can multiply a 2X3 matrix by which matrix?

2X2

2X12

3X12

2X3

Multiple Choice

When a 3x6 matrix is multiplied by a 6x5 matrix, what will the dimensions of the product be?

6x6

3x6

3x5

5x6

Multiple Choice

If the matrices can be multiplied, what are the dimensions of the product?

Matrix multiplication is not possible.

3 x 1

1 x 2

3 x 2

Multiple Choice

Find the product.

Not possible.

-3 16

17 12

8 -10

3 12

-15 -8

-1 -3

Multiple Choice

Find the product.

No Product Exists

Multiple Choice

Find the product of the matrices.

Determinants

det(A)

IAI

square

ad-bc

inverse

Multiple Choice

Find the determinant of the matrix

Multiple Choice

Solve for the determinant of the following matrix:
⌈12 −3⌉
⌊−6 15⌋
*detA= ad-bc

198

162

-333

-9

Multiple Choice

Calculate the determinant

none

-32

-8

Inverse Matrix

switch
change

Multiple Choice

What is the inverse of this matrix?

_{(1/25) (-4/25)}
_{(3/25) (13/25)}

_{(1/5) (-4/5)}
_{(3/5) (13/5)}

_{(6/25) (-2/25)}
_{(2/25) (9/25)}

_{(1/150) (-4/150)}
_{(3/150) (13/150)}

Multiple Choice

What is the inverse of the following matrix?
⌈4 −3⌉
⌊12 3⌋
*det= 38

⌈³∕₃₈ ³∕₃₈⌉
⌊−⁶∕₁₉ ²∕₁₉⌋

⌈⁴∕₃₈ −³∕₃₈⌉
⌊¹²∕₃₈ ³∕₃₈⌋

⌈²∕₁₉ −³∕₃₈⌉
⌊−⁶∕₁₉ ³∕₃₈⌋

⌈³∕₃₈ ³∕₃₈⌉
⌊−¹²∕₃₈ ⁴∕₃₈⌋

Multiple Choice

Which of the following has a determinant of 0?
*det= ad-bc

⌈1 0⌉
⌊2 3⌋

⌈-4 -2⌉
⌊6 3⌋

Multiple Choice

Which of the following is the inverse of the matrix A=
⌈3 0⌉
⌊0 2⌋
*Inverse=
¹∕detA × ⌈d −b⌉ ⌊−c a⌋

[1/2 0]
[0 1/3]

[-3 0]
[0 -2]

⌈1/3 0⌉
⌊0 1/2⌋

[2 0]
[0 3]

Multiple Choice

Are A and B inverses?
A = ⌈3 -10⌉
⌊1 4⌋
B = ⌈2/11 5/11⌉
⌊-1/22 3/22⌋
*AB=I

Yes

Matrices

Add, Subtract, Multiply, Determinant, Inverse

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