Matrix

Matrix

Introduction and Operations

Objectives

• To know the definition of a matrix

• To know the dimension of a matrix

• To know the type of matrices

• To know the equality of matrices

• Able to add and subtract two or more matrices

• Able to multiply a scalar by a matrix

Definition

• A matrix (plural matrices) or array is a set of numbers arranged in an ordered manner into rows and columns and placed within large brackets.

• Each number in the matrix is called an element. Elements can be any number including fractions.

Introduction to Matrix

Example

• There are 6 elements

• c₂₁ : element of 2^nd row, 1^st colomn = 3

• c₂₂ = 6

• Dimension = number of row by number of colomn = number of row x number of colomn

• Dimension/order/ordo of matrix C = 3 by 2 = 3x2

• C_3x2 means matrix C with dimension 3x2

Multiple Choice

What is the value of element a₂₃?

• 2

• -1

• 6

• 1

Multiple Choice

Name the dimensions:

• 6x2

• 2x6

• 12

• 36

Multiple Choice

In Matrix R (pictured) what element is r₂₃?

• 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

How many columns are there in a 5 x 4 matrix?

• 5

• 4

• 20

• 9

Multiple Choice

How many rows are in a 7 x 3 matrix?

• 7

• 3

• 21

• 10

Type of Matrices

• Square Matrix

• Diagonal Matrix

• Unit/Identity Matrix

• Zero/null Matrix

• Equal Matrices, have identical elements, i.e the same values in the same positions.

Multiple Choice

Which of the followings is True?

• x=2, y=4, z=6

• x=4, y=2, z=6

• x=2, y=6, z=4

• x=6, y=4, z=2

Multiple Choice

Find the value of x and y if they are equal matrices.

• x=2 , y=5

• x=3, y=3

• x=3, y=5

• x=5, y=3

Multiple Choice

Can the operation be performed?

• Yes

• No

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 B-A

• -3 1

  7 -1

• 1 0

  1 -4

• 4 0

  -6 1

• 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

Exercise and Homework

1. Exercise : ixl.com, Algebra 1, M.1, M.3

2. Homework : ixl.com, Algebra 1, M.4