Answer:
23. b
24. c
25. b
26. c
Step-by-step explanation:
23. In problem 21, you found the coefficient matrix to be ...
[tex]\left[\begin{array}{ccc}2&-3&1\\1&2&-4\\-3&-2&3\end{array}\right][/tex]
Its determinant is ...
(2)(2)(3) +(-3)(-4)(-3) +(1)(1)(-2) -(-3)(2)(1) -(-2)(-4)(2) -(3)(1)(-3)
= 12 -36 -2 +6 -16 +9 = -27 . . . . choice b
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24. Looking at the equation involving x11 terms, we have ...
-3x +7 = 10
-3x = 3 . . . . . subtract 7
x = -1 . . . . . . divide by -3 . . . . matches choices A and C
We note that choices A and C differ in their values for x22, so we consider the equation for that:
-3x -3 = -18
x + 1 = 6 . . . . . . . divide by -3
x = 5 . . . . . . . . matches choice C
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25. Dx will be the determinant of the matrix with the constants in the first column. Choice B is the only one that matches.
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26. The value of Dx is -78 +24 = -54. The determinant of the coefficient matrix is (5)(6) -(-3)(-4) = 30 -12 = 18. So the value of x is -54/18 = -3, which matches choice C.
