Stitz-Zeager_College_Algebra_e-book

7 systems of non linear equations and inequalities d

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Unformatted text preview: 1 3 4 19 from Exercise 1 above. (a) Show that the characteristic polynomial of G is p(λ) = −λ(λ − 1)(λ − 22). That is, compute the determinant of G − λI3 . (b) Let G0 = G. Find the parametric description of the solution to the system of linear equations given by GX = 03×3 . (c) Let G1 = G − I3 . Find the parametric description of the solution to the system of linear equations given by G1 X = 03×3 . Show that any solution to G1 X = 03×3 also has the property that GX = 1X . (d) Let G22 = G − 22I3 . Find the parametric description of the solution to the system of linear equations given by G22 X = 03×3 . Show that any solution to G22 X = 03×3 also has the property that GX = 22X . 8.5 Determinants and Cramer’s Rule 8.5.4 521 Answers 1. (a) (b) (c) (d) det(B ) = 1 det(C ) = 0 det(Q) = x2 1 det(L) = x7 (e) det(F ) = −12 (f) det(G) = 0 (g) det(V ) = 20i + 43j + 4k (h) det(H ) = −2 2. (a) x = 39, y = −13 (b) x = 7500, y = 500 76 (c) x = 47 , y = − 45 47 (d) x = 1, y = 2, z = 0 (e) x = 3. (a) x4 = 4 121 60 , y= 131 60 , z = − 53 60 (b) x4 = −1 37 5 12 4. (a) B −1 = 5 −2 (b) F −1 = 7 4 −1 6 7 2 9 −4 1 6 1 2 −1 4 1 6 5. Carl owns 78 common cards and 39 rare cards. 6. 3.125 gallons. 7. 20 7...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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