1. 4-2 Adding & Subtracting Matrices
Objective: To add and subtract matrices

2. Adding Matrices
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).
Theater C A C A
Matinee Evening
a. Write two 2  2 matrices to represent matinee and evening sales.
Theater
Theater
Matinee
C A
Theater
Theater
Evening
C A

3. Continued (continued) b. Find the combined sales for the two showings. + = =
Theater
Theater
C A

4. Finding Identity and Inverse Matrices
Find each sum.
9 0
–4 6
0 0
3 –8 –
–3 8
5 –1 a. + b. + = – =
3 + (–3) –8 + 8
– (–1) =
9 0
–4 6 =
0 0

5. Subtracting Matrices 4 8 –2 0 7 –9 4 5 A = and B = . Find A – B.
4 8
–2 0
7 –9
A = and B = Find A – B.
Method 1: Use additive inverses.
A – B = A + (–B) =
4 8
–2 0 –
–4 –5
Write the additive inverses of the elements of the second matrix.
4 + (–7)
–2 + (–4) (–5)
Add corresponding elements =
–3 17
–6 –5 =
Simplify.

6. Continued (continued) Method 2: Use subtraction. A – B = – 4 8 –2 0
4 8
–2 0
7 –9
4 – – (–9)
–2 – – 5
Subtract corresponding elements =
–3 17
–6 –5 =
Simplify.

7. Solving Matrix Equations
3 –1
10 –3 –
6 –9
Solve X – = for the matrix X.
X – =
10 –3 –
6 –9
3 –1
X – =
3 –1
10 –3 –
6 –9
Add
to each side of the equation. –
14 –9
X =
Simplify.

8. Determining Equal Matrices
Determine whether the matrices in each pair are equal.
a. M = ; N =
– –1
4 – – – 79
M = ; N =
– –1
4 – – – 7 9
Both M and N have three rows and two columns, but –
M and N are not equal matrices. 7 9 = /

9. Continued (continued) 27 9 – 16 4 3 –4 40 –3 b. P = ; Q = 8 0.2 12 4
3 –4
40 –3
b. P = ; Q = 8
0.2 12 4
P = ; Q =
3 –4
40 –3 – 27 9 16 4 12 8
0.2
Both P and Q have two rows and two columns, and their corresponding elements are equal. P and Q are equal matrices.

10. Finding Unknown Matrix Elements
Solve the equation
2m – n –3
–4m + 2n
= for m and n.
15 m + n
–30
2m – n = 15 –3 = m + n –4m + 2n = –30
2m – n –3
–4m + 2n =
15 m + n
–30
Since the two matrices are equal, their corresponding elements are equal.

11. Continued (continued) Solve for m and n. 2m – n = 15 m + n = –3
3m = 12 Add the equations.
m = 4 Solve for m.
4 + n = –3 Substitute 4 for m.
n = –7 Solve for n.
The solutions are m = 4 and n = –7.

12. Homework
Pg 178 # 2,3,4,10,11,14,17