Matrices

Matrices

Dr. Tom Giles

Multiple Choice

How many columns are in a 5 x 4 matrix?

• 5
• 4
• 20
• 9

Multiple Choice

What is the size of the matrix below? Always do Rows x Columns.

• 3 x 4

• 4 x 3

Multiple Choice

How many rows are in a 7 x 3 matrix?

• 7
• 3
• 21
• 10

Multiple Choice

What is the size of the matrix below?

• 0 x 1

• 1 x 0

• 3 x 3

• 3 x 0

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

Which element is located in A₂₃?

• -3

• 5

• -9

• 2

Multiple Choice

What is a Matrix?

• An equation of over 5 numbers or symbols 
• A set of numbers in rows and columns
• A method of finding the n^th value of a series
• A complicated number system

Multiple Choice

Subtract

• 3    -8
  0   -1

• 3   -4
  8  -13

• -3   8
  0    1

• 3   -8
  -8    1

Multiple Choice

What are the dimensions of this matrix?

• 2 x 3
• 3 x 2
• 6 x 1
• 1 x 6

Multiple Choice

Find A-B

• -3     1
  7     -1

• 1     0
  1     -4

• -4       0
  6     -1

• not possible because rows do not match columns

Multiple Choice

In Matrix R (pictured) what element is in the second row, third column?

• 8
• 9.01
• 6
• 1

Multiple Choice

Add

• 11    8
  -4     2

• 3     2
  -6    -6

• -3    2
  -4    -6

• 10    8
  -6    2

Multiple Choice

What is the value of the variable in the equation?

Multiple Choice

Add

• 11    8
  -4     2

• 3     2
  -6    -6

• -3    2
  -4    -6

• 10    8
  -6    2

Multiple Choice

What is the value of element M_3,4?
(Think about what is in the 3rd row and 4th column)

• 34
• 42
• 37
• π

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

Find A+B

• 8     10
  8      1 
• 12     25
  7     1
• 10     30
  0     1
• can't add two together because the rows dont match columns

Multiple Choice

What is the location of 5?

• A₁₂

• A₂₁

• A₂₅

• A₁₃

Multiple Choice

Find B-A

• -4     0
  6     -1
• 1     0
  1     -4
• 4       0
  -6     1
• not possible because rows do not match columns

Match

Match each matrix to its correct dimension.

1 x 3

3 x 1

2 x 4

4 x 2

2 x 3

• 1 x 3

• 3 x 1

• 2 x 4

• 4 x 2

• 2 x 3

Multiple Choice

Add

• 11    8
  -4     2
• 3     2
  -6    -6
• -3    2
  -4    -6
• 10    8
  -6    2

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

Subtract

• -5
  -8
  3
  10
• -9
  8
  3
  2
• 5
  -8
  3
  10
• -5
  8
  3
  2

Multiple Choice

Find the product of the two matrices.

• 17 12

  25 18

• 17 12

  12 6

• 17 12

  7 5

• 17 12

  10 12

Multiple Choice

Subtract

• 3    -8
  0   -1
• 3   -4
  8  -13
• -3   8
  0    1
• 3   -8
  -8    1

Multiple Choice

find: B*A

• 47     30
  9     5

• 17     15
  42     35

• 10     25
  7     1

• not possible because rows do not match columns

Multiple Choice

What values of x and y make the equation true?

• x = 5

  y = -2

• x = 3

  y = -5

• x = 9

  y = 10

• x = 16

  y = -5

Multiple Choice

These matrices are being multiplied. Determine the dimension/size of the new matrix. 

• Can't multiply them

• 4  x  2

• 3  x  3

• 4  x  3

Multiple Choice

What is the name of each entry of a matrix?

• Row
• Element
• Dimension
• Rectangle

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

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

Multiple Choice

What values of x and y make the equation true?

• x = 5

  y = -2

• x = 3

  y = -5

• x = 9

  y = 10

• x = 16

  y = -5

Multiple Choice

Add.

• -2   4   -9
  -1   -6   -17
• -8   12   -9
  1   6   17
• -8   4   -9
  15   6   7
• -2   -4   -9
  15   6    7

Multiple Choice

What is the value of the variable in the equation?

Multiple Choice

What comes first in the order?

• Row
• Column
• The Egg
• The Chicken

Multiple Choice

What values of x and y make the equation true?

• x = 0

  y = 3

• x = 2

  y = 2

• x = 4

  y = 3

• x = 7

  y = 4

Multiple Choice

Solve for matrix X.

• -9

  5

  3

• 9

  13

  -9

• 15

  -5

  3

• 10

  4

  6

Multiple Choice

What number is located at D_2,1?

• 6

• -4

• 2

Multiple Choice

Solve for matrix Y.

• -4    9
  -11    9
• 4   -8
  11   8
• 4   -9
  11   9
• -4   9
  11   -9

Multiple Choice

What number is located at A_2,2?

• -1

• 2

• 5

• -3

Multiple Choice

• A

• B

• C

• D

Multiple Choice

What are the dimensions of matrix D?

• 1 x 3

• 3 x 1

Multiple Choice

• A

• B

• C

• D

Multiple Choice

What are the dimensions of matrix F?

• 1 x 3

• 3 x 1

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Add

• 11    8
  -4     2
• 3     2
  -6    -6
• -3    2
  -4    -6
• 10    8
  -6    2

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Subtract

• 3    -8
  0   -1
• 3   -4
  8  -13
• -3   8
  0    1
• 3   -8
  -8    1

Multiple Choice

• A

• B

• C

• D

Multiple Choice

You can multiply a 2X3 matrix by which matrix?

• 2X2
• 2X12
• 3X12
• 2X3

Multiple Choice

What do m, n, p and q equal in this scalar matrix multiplication?

• m=8, n=9, p=-4, q=4 
• m=15, n = -45, p=20, q=-5
• m=20, n=-5, p=15, q=-45
• m=-5, n=20, p=-45, q=15

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

In Matrix R (pictured) what element is a₂₃?

• 8
• 9.01
• 6
• 1

Multiple Choice

Find A+B

• 8     10
  8      1 
• 12     25
  7     1
• 10     30
  0     1
• can't add two together because the rows dont match columns

Multiple Choice

Find the product of the two matrices.

• undefined
• -3   16
  17   12
  8   -10
• 3   12 
  -15  -8
  -1   -3

Multiple Choice

Dimensions?

• a
• b
• c
• d

Multiple Choice

Find the product of the two matrices.

• 1   2
  6   -8
• -3   -5
  -5   -11
• -2     8
  -6   -12
• 2  -3
  5   -2

Multiple Choice

Find the values of x, y and z.

• 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

Multiple Choice

find: B*A

• 47     30
  9     5
• 17     15
  42     35
• 10     25
  7     1
• not possible because rows do not match columns

Multiple Choice

Find A-B

• -3     1
  7     -1
• 1     0
  1     -4
• -4       0
  6     -1
• not possible because rows do not match columns

Multiple Choice

These matrices are being multiplied. Determine the dimension/size of the new matrix. 

• Can't multiply them
• 4  x  2
• 3  x  3
• 4  x  3

Multiple Choice

What comes first in the order?

• Row
• Column

Multiple Choice

Find the product of the matrices.

• A
• B
• C
• D

Multiple Choice

Can the operation be performed?

• Yes

• No

• Sometimes

• Only Mr. Dasal knows

Multiple Choice

Perform scalar multiplication on the matrix

• A
• B
• C
• D

Multiple Choice

How many columns are in a 5 x 4 matrix?

• 5
• 4
• 20
• 9

Multiple Choice

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

These matrices are being multiplied. Determine the dimension/size of the new matrix. 

• Can't multiply them
• 4  x  2
• 3  x  3
• 4  x  3

Multiple Choice

Subtract

• 3    -8
  0   -1
• 3   -4
  8  -13
• -3   8
  0    1
• 3   -8
  -8    1

Multiple Choice

Find the product of the two matrices.

• undefined
• -3   16
  17   12
  8   -10
• 3   12 
  -15  -8
  -1   -3

Multiple Choice

What is a Matrix?

• An equation of over 5 numbers or symbols 
• A set of numbers in rows and columns
• A method of finding the n^th value of a series
• A complicated number system

Multiple Choice

Find the product of the two matrices.

• 1   2
  6   -8
• -3   -5
  -5   -11
• -2     8
  -6   -12
• 2  -3
  5   -2

Multiple Choice

How many rows are in a 7 x 3 matrix?

• 7
• 3
• 21
• 10

Multiple Choice

find: B*A

• 47     30
  9     5
• 17     15
  42     35
• 10     25
  7     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

Find the product of the two matrices.

• undefined
• -3   16
  17   12
  8   -10
• 3   12 
  -15  -8
  -1   -3

Multiple Choice

Multiple Choice

Find the product of the two matrices.

• 1   2
  6   -8
• -3   -5
  -5   -11
• -2     8
  -6   -12
• 2  -3
  5   -2

Multiple Choice

You are treating your friend to lunch today. Which restaurant would cost the least for each of you to have an order of chicken tender, fries and a soda? And how much would that cost before tax?

• Bojangle's $16.74

• Chick fil a $13.83

• Zaxby's $17.86

• Chick fil a $15.66

Multiple Choice

find: B*A

• 47     30
  9     5
• 17     15
  42     35
• 10     25
  7     1
• not possible because rows do not match columns

Multiple Choice

Perform the indicated operation

• not possible

Multiple Choice

Find the product of the matrices.

• A
• B
• C
• D

Multiple Choice

Perform the indicated operation

• not possible

Multiple Choice

Can the operation be performed?

• Yes
• No
• tomato
• Maybe

Multiple Choice

Perform the following operation

• not possible

Multiple Choice

Can we multiply the two matrices below?

• Yes, it is DEFINED.

• No, it is UNDEFINED.

Multiple Choice

What do a, b, c and d equal in this matrix addition?

• a = -1, b = 10, c = 7, d = -11
• a = -1, b = 10, c = -11, d = 7
• a = 10, b = -1, c = 7 , d = -11 
• a = 10, b = -1, c = -11, d = 7

Multiple Choice

Find the product of the two matrices.

• 17 12

  25 18

• 17 12

  12 6

• 17 12

  7 5

• 17 12

  10 12

Multiple Choice

Calculate the following scalar multiplication.

Multiple Choice

Calculate the following scalar multiplication.

Multiple Choice

Due to inflation, these restaurants must increase their prices by 5%. Which matrix represents the new menu prices?

Multiple Choice

What are the dimensions of this matrix?

• 2 x 3
• 3 x 2
• 6 x 1
• 1 x 6

Multiple Choice

What comes first in the order?

• Row
• Column