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Types of Matrices + Rules
Operations with Matrices
Matrix Multiplication
Problem Solving w/Matrices
100
A matrix is defined by n x m. What do n & m represent?
n = rows m = columns
100

The size or dimension of a matrix is the number of rows and the number of columns, written in that order, and in the format m × n, read "m by n." If n = m, which means that the number of rows equals the number of columns, then the matrix is called a

Square Matrix

100
Given matrix A: 3A would be considered what type of matrix multiplication?
Scalar Multiplication
100
Can you find the inverse of a rectangular matrix?
No, only square matrices
200
Define a row & a column matrix
Row matrix has only one row. A column matrix only has one column
200
When adding or subtracting matrices, you need to add/subtract the corresponding elements of the respective matrices. True or False
True
200

3 [12   -3   5] is?

[36 -9 15]

200
If the determinant equals zero, what does that indicate?
No inverse exists.
300
What is an identity matrix?
A square matrix with all elements from the top left to bottom right being one's. Every other element is zero.
300

[7   11] - [-1   3]

[8   8]

300
Multiplying any square matrix by the corresponding square identity matrix will yield what?
The original matrix.
300

What is the inverse of the 2x2 matrix

[1   2]

[3   4]

[-2        1]

[1.5   -0.5]

400
What must occur for you to be able to add or subtract matrices?
The dimensions of the matrices must be the same.
400

Subtraction of Matrices [7] - [8] - [0] - [-5] = ?

[4]

400

Multiplying matrices [3 5 9 0 0 1 2 ] x [2]

Not possible

400

Represent these simultaneous equations in matrix form:

4x - 3z = 4

3x - z = -5

[4   -3]   [x]   =  [4]

[3    -1]   [z]  =   [-5]

500
Matrix A has the dimensions 4 x 5 Matrix B has the dimensions 5 x 1. Can matrix AB be multiplied? Explain why.
Yes they can as the columns in Matrix A match the rows in Matrix B. The final dimensions of AB would be 4 x 1.
500

In the first game of the netball season, Ms Graham scores 11pts, has 6 assists and 3 rebounds. Represent this information as a matrix. In the second game she scores 14pts, has 4 assists and 4 rebounds. Represent this information as a matrix. What are her totals after two games?

Pts = 25 Assists = 10 Rebounds = 7

[25   10  7]

500

Tickets to the movie IT costs $20.00 for adults, $10.00 for children and $12.50 for seniors. Create a column matrix to represent this information. For opening night, 145 adults, 2 children and 32 seniors attend. Represent this information as a row matrix. Find the product of the two matrices to find the total earning made by the cinema

$3320.00

500

Ms Gregory sells 4 of her brownies and 3 cookies for $15. The following week she sells 6 of her brownies and 5 cookies for $23.50. Create a matrix to represent this information. Solve for how much each brownie and cookie costs.

Brownie = $2.25 Cookie = $2.00