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Stitz-Zeager_College_Algebra_e-book

# 7 systems of non linear equations and inequalities

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Unformatted text preview: such that M −1 also has integer entries and then use your matrix to encode the message. 9 10 Misty Mushrooms and Sun Berries are the only known ﬁctional sources of Vitamin X. Vitamin X is needed to sustain Sasquatch longevity only. 8.4 Systems of Linear Equations: Matrix Inverses 8.4.2 507 Answers 1. (a) A−1 = −2 1 −5 2 3 2 −1 2 (f) F −1 = 7 4 −1 6 37 5 12 (c) C is not invertible 9 1 −2 (d) D−1 = 2 8 −1 −1 8 4 (e) E −1 = 1 −3 −1 1 −6 −3 (b) B −1 = 7 2 −9 4 1 6 1 2 1 −4 1 6 (g) G is not invertible 16 0 3 −90 − 1 − 35 2 2 (h) H = 5 0 1 −36 0 −7 0 7 2 0 1 2. The coeﬃcient matrix is B −1 from Exercise 1 above so the inverse we need is (B −1 )−1 = B . The solutions to the systems are (a) 12 −7 −5 3 26 39 = 39 −13 So x = 39 and y = −13. (b) 12 −7 −5 3 0 −1 = 7 −3 So x = 7 and y = −3. (c) 12 −7 −5 3 −7 5 = −119 50 −1 8 3. (a) 1 −3 1 −6 −1 8 1 −3 (b) 1 −6 −1 8 (c) 1 −3 1 −6 4 −1 −3 4 −1 −3 4 −1 −3 1 0 = 0 0 1 = 0 0 0 = 1 S...
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