Question

For the following exercises, solve a system using the inverse of a 3 x 3 matrix. 16.4x + 4y + 4z = 40 4 4 х 140 2x - 3y + 4z = -12 -3 4 y - x + 3y + 4z = 9 -1 3 4 2 -12 2 G

Answer 1

soln: Given susten of Equations 4 n +44 +43 = 40 20-34 4 4 3 =-12 anty 443 = 9 The matsin equation of siven system of equations is AX-B, where 2-3 3 3) 2 and [ -12 q Since and DI AX=B =) X = A'B. Adja. deta der Aca(-12-12] -4 [8+4]+456-3] åbna6+12a-96-48 +12 det A=-132 €0, hi enists. T . Adja A = c cofactor matsin of A) All A12 A13 iti A ij = (-1) mij Ari A 22 A31 A32 A33 T 11 A23 T -24 -12 11 3 -16 20 28 8 n20 -24 =) Adj A = .u 20 28 -8 - 1.2 3 -16 -20 TA pl -24-4 I deta Adja - 132 -4 28 -12 20 -8 3 -16 -20

since x = x = ÀR hて - -4 28 20 -8 -16 -20 uo -12 -12 3 132 -660 -792 -- -1 132 -960 +48 +252 -240 -72 120 +312 - 180 -480 132 132 S Х a 6 +660 I132 1921132 1321132 - 1 The solutions n=5, y=6,3=-4