Matrices Precalculus

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

3

1

8

19

Multiple Choice

How many rows are in a 7 x 3 matrix?

• 7
• 3
• 21
• 10

Multiple Choice

How many columns are in a 5 x 4 matrix?

• 5
• 4
• 20
• 9

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?

• 2
• -1
• 6
• 1

Multiple Choice

Element G₂₂ is

• 1

• 2

• 3

• 4

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.

• A
• B
• C
• D

Determinants

det(A)

IAI

square

ad-bc

inverse

Multiple Choice

Find the determinant of the matrix

• A
• B
• C
• D

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

• 0
• 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
• No