Calculations with Matricies

Matrices

​Dr. Tom Giles

Adding & Multiplying Matrices

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

What are the dimensions of this matrix?

• 2 x 3

• 3 x 2

• 6 x 1

• 1 x 6

Multiple Choice

How many rows are in a 7 x 3 matrix?

• 7
• 3
• 21
• 10

Multiple Choice

Add

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

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

Can the operation be performed?

• Yes

• No

• Sometimes

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

How many columns are in a 5 x 4 matrix?

• 5
• 4
• 20
• 9

Multiple Choice

Subtract

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

How many columns are in a 5 x 4 matrix?

• 5
• 4
• 20
• 9

Multiple Choice

Perform the indicated operation

• not possible

Multiple Choice

Name the dimensions:

• 6x2
• 2x6
• 12
• 36

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

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 are the dimensions of this matrix?

• 2 x 3
• 3 x 2
• 6 x 1
• 1 x 6

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 B-A

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

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

Dimensions?

• a
• b
• c
• d

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

Perform the indicated operation

• not possible

Multiple Choice

How would a scalar multiplication be carried out for a matrix?

• Add the Scalar to every element in the matrix
• Dot product the rows of one matrix with the columns of the other matrix
• Multiply every element with the scalar to create a new matrix
• subtract the elements in the first matrix from the elements of the second matrix

Multiple Choice

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

Add.

• Correct answer not given

Multiple Choice

Subtract

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

Multiplying Matrices

Multiple Choice

Perform the matrix multiplication, if possible.

• Cannot be multiplied, dimensions not compatible.

Multiple Choice

Perform the matrix multiplication, if possible.

• Cannot be multiplied, dimensions not compatible.

Multiple Choice

Perform the matrix multiplication, if possible.

• Cannot be multiplied, dimensions not compatible.

Multiple Choice

What is A^-1?

Multiple Choice

Are these two matrices inverses of each?

• Yes

• No

• I don't know

• maybe

Multiple Choice

Are these matrices inverses of each other?

• No

• Yes

• Maybe

• I don't know

Multiple Choice

Determine if the matrix has an inverse, if so find it.

• No
•  0   1
  -1   2
• -1   3
    1   -2
•   2   -1
  -1   1