02/12/2024 - Unit 5 - Matrices Intro Lesson

What is a matrix?

A matrix is a rectangular form of data.

Matrices

• Are used by Netflix and Hulu to recommend videos for you

• Help solve higher Algebra problems such as Quadratics.

• Are used in computer graphics and video games.

Matrices

Can have either brackets of parenthesis.

A Matrix is comprised of....

• Rows

• Columns

• Elements

Size of a Matrix

The size is determined by the number of rows x number of columns. Only like size matrices can be added or subtracted from one another.

Multiple Choice

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

• 3 x 4

• 4 x 3

Multiple Choice

What is the size of the matrix below?

• 0 x 1

• 1 x 0

• 3 x 3

• 3 x 0

Identifying Elements in a Matrix

We use subscript to identify the location of an element in a matrix. It is the name of the matrix followed by row x column. Rows are top to bottom and columns are left to right.

Multiple Choice

Which element is located in A₂₃?

• -3

• 5

• -9

• 2

Multiple Choice

Subtract

• 3    -8
  0   -1

• 3   -4
  8  -13

• -3   8
  0    1

• 3   -8
  -8    1

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

Add

• 11    8
  -4     2

• 3     2
  -6    -6

• -3    2
  -4    -6

• 10    8
  -6    2

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

What is the location of 5?

• A₁₂

• A₂₁

• A₂₅

• A₁₃

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

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.

​Multiplying Matrices

Once we know we can multiply matrices, then we can start the process. First, highlight the first row in the first matrix and the first column in the second matrix. Multiply the first terms, then the second terms, and then the third terms, and so on. Add the products of each multiplication and that is the first term in the product matrix.

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

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

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