12.1 Intro to Matrices

What is a matrix?

A matrix is a rectangular pattern of data with rows and columns. It's similar to a table, but without the headings.

A matrix has

• rows

• columns

• elements

Dimensions

The dimensions of a matrix are read ROW by COLUMN.

Multiple Choice

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

• 8
• 9.01
• 6
• 1

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 name of each entry of a matrix?

• Row
• Element
• Dimension
• Rectangle

Multiple Choice

Dimensions?

• a
• b
• c
• d

Multiple Choice

What comes first in the order?

• Row
• Column

​Elements of a Matrix

It's important to be able to identify specific elements of a matrix. Look at the diagram to see how it's done, and then practice for yourself!

Multiple Choice

In Matrix R (pictured) what element is a₂₃?

• 8
• 9.01
• 6
• 1

Multiple Choice

What is the entry at f₄₂?

• 23

• -81

• -44

• 99

• -56

To add or subtract two matrices...

they must be the SAME size. If the dimensions are the same, then you add/subtract the corresponding elements.

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

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

Subtract

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

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

Can the operation be performed?

• Yes

• No

• Sometimes

• only Mrs. Brewer knows

Scalar Multiplication

This is very simple...just distribute the scalar to each element!

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 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