In Exercises 24–29 , solve by Cramer’s rule, where it applies − x 1 − 4 x 2 + 2 x 3 + x 4 = − 32 2 x 1 − x 2 + 7 x 3 + 9 x 4 = 14 - x 1 + x 2 + 3 x 3 + x 4 = 11 x 1 − 2 x 2 + x 3 − 4 x 4 = − 4
In Exercises 24–29 , solve by Cramer’s rule, where it applies − x 1 − 4 x 2 + 2 x 3 + x 4 = − 32 2 x 1 − x 2 + 7 x 3 + 9 x 4 = 14 - x 1 + x 2 + 3 x 3 + x 4 = 11 x 1 − 2 x 2 + x 3 − 4 x 4 = − 4
For Exercises 115–120, factor the expressions over the set of complex numbers. For assistance, consider these examples.
• In Section R.3 we saw that some expressions factor over the set of integers. For example: x - 4 = (x + 2)(x – 2).
• Some expressions factor over the set of irrational numbers. For example: - 5 = (x + V5)(x – V5).
To factor an expression such as x + 4, we need to factor over the set of complex numbers. For example, verify that
x + 4 = (x + 2i)(x – 2i).
115. а. х
- 9
116. а. х?
- 100
117. а. х
- 64
b. x + 9
b. + 100
b. x + 64
118. а. х — 25
119. а. х— 3
120. а. х — 11
b. x + 25
b. x + 3
b. x + 11
please solve asap
Example 4.8.2 Simplify the following expressions:
(a) Cov(8.X +3,5Y – 2), (b) Cov(10X-5, -3X + 15), (c) Cov(X+2,10X-3Y), (d) p10X,Y+4-
Algebra and Trigonometry: Structure and Method, Book 2
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