**Unformatted text preview: **roof of Theorem 8.9 is, like so many of the results in this section, best left to a course in
Linear Algebra. In such a course, not only do you gain some more sophisticated proof techniques,
you also gain a larger perspective. The authors assure you that persistence pays oﬀ. If you stick
around a few semesters and take a course in Linear Algebra, you’ll see just how pretty all things
matrix really are - in spite of the tedious notation and sea of subscripts. Within the scope of this
text, we will prove a few results involving determinants in Section 9.3 once we have the Principle of
Mathematical Induction well in hand. Until then, make sure you have a handle on the mechanics
of matrices and the theory will come eventually. 8.5 Determinants and Cramer’s Rule 8.5.3 517 Exercises 1. Compute the determinant of the following matrices. (Some of these matrices appeared in
Exercise 1 in Section 8.4.) 12 −7
123
(a) B =
−5
3
(f) G = 2 3 11 3 4 19
6 15
(b) C = 14 35
i
j
k
0
5
(g) V = −1
x x2...

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