This document discusses matrices and matrix operations. It defines a matrix as a rectangular arrangement of numbers, with elements as the individual numbers. A matrix has m rows and n columns, written as m x n. Two matrices are equal if they have the same dimensions and corresponding elements are equal. Matrices can only be added or subtracted if they have the same dimensions. To multiply a matrix by a scalar, each element is multiplied by the scalar. The document also provides an example of matrices representing sales data for small and large steel DVD racks in different wood types last month and this month. It asks to find the average monthly sales for the two month period using the matrices. Finally, it gives a matrix equation to solve for x.

1. 10.1 matrix operations.notebook April 05, 2013
matrix ­ a rectangular arrangement of numbers
element ­ each number in the matrix
dimensions of a matrix ­ m rows and n columns ­ m x n (read m by n)
Two matrices are equal if their dimensions are the same and the elements in
corresponding positions are equal.
Tell whether the matrices are equal. Explain.
[ ] [ ]
2 0
0 ­ 2
2 0
0 ­ 2 [ ][ ]
1 ­1 1 (4 ­ 5)
0 4/2 0 (3 ­ 1)
[ 1 3]
[]
1
3

2. 10.1 matrix operations.notebook April 05, 2013
You can add and subtract matrices only if they have the same dimensions.
[][]2 4
1 + ­1
3 5
[ ][ ] [
4 ­ 1 ­ 1 2
0 5 ­2 3 ][]
3 ­11 1
­
12 ­2 15

3. 10.1 matrix operations.notebook April 05, 2013
To multiply a matrix by a scalar (real number), you multiply
each entry in the matrix by the scalar.
[ ]
3 0
­1 ­2 1 [ ]
­1 4
2 0 3

4. 10.1 matrix operations.notebook April 05, 2013
A store sells small and large steel DVD racks with wooden bases. Each size
is available in three types of wood: walnut, pine, and cherry. Sales of the racks
for last month and this month are shown.
Last month (A) This month (B)
Small Large Small Large
[ ]
Walnut 12 11
Pine 28 20
Cherry 22 21 [ ]
Walnut 14 15
Pine 36 28
Cherry 20 17
Use the matrices to find the average monthly sales for the two month period.

5. 10.1 matrix operations.notebook April 05, 2013
Solve the matrix equation for x.
[ 2x ­1
3 0 ]+[
3 15] [
4 ­1
=
12 ­2
]
6 15