Adding and Subtracting Matrices

1
Section 4.2

• Adding and Subtracting Matrices

2
Adding and Subtracting Matrices
ALGEBRA 2 LESSON 4-2
The table shows information on ticket sales for
a new movie that is showing at two theaters.
Sales are for children (C) and adults (A).
a. Write two 2 ? 2 matrices to represent matinee
and evening sales.
4-2
3
Adding and Subtracting Matrices
ALGEBRA 2 LESSON 4-2
(continued)
b. Find the combined sales for the two showings.
4-2
4
Adding and Subtracting Matrices
ALGEBRA 2 LESSON 4-2
Find each sum.
9 0 4 6
0 0 0 0
3 8 5 1
3 8 5 1
a.
b.


4-2
5
Adding and Subtracting Matrices
ALGEBRA 2 LESSON 4-2
4 8 2 0
7 9 4 5
A and B .
Find A B.
Method 1 Use additive inverses.
4-2
6
Adding and Subtracting Matrices
ALGEBRA 2 LESSON 4-2
(continued)
Method 2 Use subtraction.
4-2
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Adding and Subtracting Matrices
ALGEBRA 2 LESSON 4-2
2 5 3 1 8 0
10 3 4 9 6 9
Solve X
for the matrix X.
4-2
8
Adding and Subtracting Matrices
ALGEBRA 2 LESSON 4-2
Determine whether the matrices in each pair are
equal.
4-2
9
Adding and Subtracting Matrices
ALGEBRA 2 LESSON 4-2
(continued)
27 9
16 4

3 4 40 3
b. P Q
12 4
Both P and Q have two rows and two columns, and
their corresponding elements are equal. P and Q
are equal matrices.
4-2
10
Adding and Subtracting Matrices
ALGEBRA 2 LESSON 4-2
Solve the equation
Since the two matrices are equal, their
corresponding elements are equal.
4-2
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Adding and Subtracting Matrices
ALGEBRA 2 LESSON 4-2
(continued)
Solve for m and n. 2m n 15 m n
3
4 n 3 Substitute 4 for m.
n 7 Solve for n.
The solutions are m 4 and n 7.
4-2
12
Adding and Subtracting Matrices
ALGEBRA 2 LESSON 4-2
Find each sum or difference. 1.
2.
3 1 4 8 5 4
3 2 9 5 4 6
2 8 0 12
9 6 6 5
3. What is the additive identity for 2 ? 4
matrices? 4. Solve the equation for x and
y. 5. Are the following matrices
equal? 6. Solve X
for the matrix X.
2x 1 5 x y
18 3x 4y x 2y 16
x 9, y 7

3 0.5
6 2
0.50 0.4 0.6

2 5
2 3
4 3 1 5
2 7 0 6
4-2