College Algebra, 2013a

8.5 Determinants and Cramer’s Rule 623
8.5.3 Exercises
In Exercises 1 - 8, compute the determinant of the given matrix. (Some of these matrices appeared
in Exercises 1 - 8 in Section 8.4.)
1. B =
[ 12 −7
−5 3
[ ] x x
2
3. Q =
1 2x
⎡
5. F = ⎣
⎡
7. V = ⎣
]
4 6 −3
3 4 −3
1 2 6
⎤
i j k
−1 0 5
9 −4 −2
2. C =
[ 6 15
14 35
⎡
1
4. L = ⎢ x 3
⎣
− 3 x 4
⎦ 6. G = ⎣
⎤
⎦ 8. H =
⎡
⎡
⎢
⎣
]
1 2 3
2 3 11
3 4 19
⎤
ln(x)
x 3
⎥
1 − 3ln(x)
⎦
x 4
⎤
⎦
1 0 −3 0
2 −2 8 7
−5 0 16 0
1 0 4 1
⎤
⎥
⎦
In Exercises 9 - 14, use Cramer’s Rule to solve the system of linear equations.
9.
11.
13.
{ 3x +7y = 26
5x +12y = 39
{
⎧
⎨
⎩
x + y = 8000
0.03x +0.05y = 250
x + y + z = 3
2x − y + z = 0
−3x +5y +7z = 7
10.
12.
14.
{ 2x − 4y = 5
10x +13y = −6
{ 1
2 x − 1 5 y = 1
6x +7y = 3
⎧
⎨
⎩
3x + y − 2z = 10
4x − y + z = 5
x − 3y − 4z = −1
In Exercises 15 - 16, use Cramer’s Rule to solve for x 4 .
15.
⎧
⎪⎨
⎪⎩
x 1 − x 3 = −2
2x 2 − x 4 = 0
x 1 − 2x 2 + x 3 = 0
−x 3 + x 4 = 1
16.
⎧
⎪⎨
⎪⎩
4x 1 + x 2 = 4
x 2 − 3x 3 = 1
10x 1 + x 3 + x 4 = 0
−x 2 + x 3 = −3