Intro Matrices

What is a matrix?

A matrix is a rectangular form of data.

Matrices

Can have either brackets of parenthesis.

A Matrix is comprised of....

• Rows

• Columns

• Elements

Size (dimension)of a Matrix

The size (dimension) or the order of the matrix 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

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

Which element is located in A₂₃?

• -3

• 5

• -9

• 2

Multiple Choice

What is the location of 5?

• A₁₂

• A₂₁

• A₂₅

• A₁₃

We use matrices to help in solving systems of equations

Here is an example of a coefficient matrix. You will have an x column and a y column and their sign must come with.

Equal Matrices

To add or subtract matrices A and B, add or subtract the corresponding elements.

Corresponding elements are elements in the same position in each matrix. 

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 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

Add

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

Multiple Choice

Subtract

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

Multiple Choice

Subtract

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

Multiple Choice

Multiply

• 25
  25
  5
• -25
  25
  -5
• -10
  -10
  -6
• 10
  10
  6