Question

[4 -2 0] 1. Use Gaussian reduction to find the determinant of A = |2 -1 2]. 11 5 7 [4 -2 01 2. Use the permutation expansion to find the determinant of A = 2 -1 2. 11 5 7

Answer 1

- l. het A=1 4 -2 o 1 & 1 of 1 1. Li 57 و مو لد by haussian Reduction method : [ Comuout the matriu into the row echelon form applying Ra Ra - (2) R, ~ l I 5 7 / applying R3 - Rz - 1 4 R ra -2 o 2 ostos ܝܐ ܠܟ R₂ H Ra ni 4 -2 , ܢܝ Cela Lo 0 -2 J . 1 4-4'01 lura 0 la - 21 = lo & 7 i5 71Jo 0 - 2 : 4x!!*(-) = -44.

op By permutation Expansion ; 0 li 0 0 1 = (4)(-1)(7) 01 01 +(4)(235) .100 16+ 2 & 1 0 (9164-2009 | : : 8/1090 18 ( 2)(7) 0 0 / +(2)2)(1) loo 1 looi + (0) (2) (5) llo 014 010) (O) (-1 (1) lolo | 0 0 1 = (4)(1)(7) · 1 + (4) (2)/5). (-1) + (-2)(a)(7)(-1) + (-2)(a)(0) .1 + 0) (2) (3) (0) + (0) (-1) (1). : -28 + (-40) + 28 - 4 toto = -44.