s
Section 5.7 Matrices
461
S e c t I o n 5 . 7 Review
technIQueS
• Add, subtract, multiply, and perform scalar multiplication on matrices.
• Solve systems of linear equations using Gaussian
elimination.
• Perform Boolean and, or, and matrix multiplication
on Boolean matrices.
maIn IDeaS
• Matrices are rectangular arrangements of data that
are used to represent information in tabular form.
• Matrices have their own arithmetic, with operations of addition, subtraction, multiplication, and
scalar multiplication.
• Systems of linear equations can be solved by performing elementary row operations on an augmented matrix (Gaussian elimination).
• Boolean matrices can be manipulated using Boolean
operations of and, or, and Boolean multiplication.
exeRcISeS 5.7
1. For the matrix:
a = £
1 2
3 0
−4 1
§
What is a 12 ? What is a 31 ?
2. Find x and y if
c
1
3
x x + y
d = c
1 3
2 6
d
3. Find x, y, z, and w if
c
x + y 2x − 3y
z − w
z + 2w
d = c
4 −7
−6
6
d
4. If a is a symmetric matrix, find u, v, and w:
a = £
2
w u
7
0
v
1 −3 4
§
For Exercises 5–7, assume the following:
r = 3, s = −2,
a = £
2 1
−1 0
3 4
§ b = £
4
1 2
6 −1 5
1
3 2
§ C = c
2
4
6 −1
d D = £
4 −6
1
3
2 −1
§
5. Compute (if possible)
a. a + D
b. a − D
c. rb
d. sC
e. a + rD
W
W