Download Objective: Students will be able to find the sum and difference of two

Objective: Students will be able to find the sum
and difference of two matrices and find the
scalar multiple of a matrix.

A matrix is

Each value in the matrix is called an _________________________.
 A matrix can be described by its _______________________. It is described by the
amount of rows times the amount of columns.

A matrix that has only one row is called

A matrix that has only one column is called
Example 1: State the dimensions of each matrix.
Each element in the matrix can be described by two indexes: the row index i and the
column index j. In the first matrix, element a23 refers to the entry in the second row,
third column or -- a23=
Example 2: Draw a column matrix with 5 rows.
Example 3: Draw a row matrix with three columns.
Matrix addition is done element-wise. Matrices can only be added or subtracted if
they have the same dimensions.
Example 4:
All we need to do is add the corresponding elements and then simplify. The same
works for subtraction.
Example 5:
Sometimes it is not possible to add or subtract matrices. This will happen if the
matrices do not have the same dimensions. You must then state it is not possible.
Example 6:
You can multiply any matrix by a constant called a scalar. This operation is called
scalar multiplication.
Example 7:
Name:
Advanced Algebra 2
Matrices Homework
Use the matrices to find the following. If the matrix does not exist, write impossible.
1. A + B =
2. B – A =
3. A – C =
4. 5A=
5. 2A – B =
6. B – 3C =
7. -½C+2C=
8. 4A+2B=
9. (A-B)+3B=
10. (2A-B)+A=
You can only multiply matrices if
# columns in the
First Matrix
=
# rows in the
Second Matrix
The product of the matrices will have the dimensions:
(rows of first matrix) x (columns of second matrix)
Example 1: If A is a 2x5 matrix and B is a 5x4 matrix, can they be multiplied? If
possible, what would be the dimensions of the resulting matrix?
Example 2: If A is a 1x3 matrix and B is a 4x3 matrix, can they be multiplied? If
possible, what would be the dimensions of the resulting matrix?
When you multiply matrices, you follow the pattern below
a b  x y  a x  b x a y  b y 
 1 1   1 1   1 1 1 2 1 1 1 2 

a2 b2
 
x 2 y 2
 
a2 x1  b2 x 2 a2 y1  b2 y 2 

In other words, multiply the elements of each row of the first matrix by the
 column in the second matrix and add the products.
elements of each
Example 3: Find AB
Example 4:
Example 5:
Please note, multiplying matrices is not commutative! Think about it…
Look at example 4, the product of a (3x3) matrix and a (3x2) matrix is a (3x2)
matrix. But what happens if we reversed the order…