FIN 502 Study Guide - Midterm Guide: Diagonal Matrix, Invertible Matrix, Diagonalizable Matrix

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10 Oct 2017
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Let a, b and c be the n x n matrices such that: det(a) = -2, det(b) = 3 and det(c) = -4. =det(a) x det(b)2 x [1/det(b)] x [1/det(c)] x det(c) det(a) x det(b) Solve the following system of li(cid:374)ea(cid:396) e(cid:395)uatio(cid:374) usi(cid:374)g c(cid:396)a(cid:373)e(cid:396)"s rule: X1 + x2 3x3 = 2 a = 1 1 -3 x = x1 b = 2. 2x1 x2 + 5x3 = 9 2 -1 5 x2 9. X2 + x3 = 3 0 1 1 x3 3 det(a) = (a31)(c31) + (a32)(c32) + (a33)(c33) = 0 + (1)(-1)3+2 det 1 -3 + (1)(-1)3+3 det 1 1. M1 = 2 1 -3 det(m1) = (a11)(c11)+(a12)(c12)+(a13)(c13) 9 -1 5 = (2)(-1)1+1 det -1 5 + (1)(-1)1+2 det 9 5 + (-3)(-1)1+3 det 9 -1. = (2)(1) [(-1)(1) (5)(1)] + (1)(-1) [(9)(1) (5)(3)] + (-3)(1) [(9)(1) (-1)(3)] M2 = 1 2 -3 det(m2) = M3 = 1 -3 2 det(m3) =

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