Question

QUESTION 7 Solve for (x, y, z), if there is a solution to the given system of linear equations: - 4x + 2y + z = 1 X- y + 3z = -5 3x + y - 4z = 10 (-1,-3, 1)) (1,3,-1) No Solution (1,3,1)

Answer 1

from the له حج 5 1 3 Z 3 4 2 3 1 from the resultant maori RCAS = 3, RCA1B) = 3 Given system of listent enerons : 424 24+ z = 1 1-4+3z = 5 3x+y- 4z=10 ervrions -4 -4 Augun ensed Matrix (Alts] can be writenos (AIB) 4. 4. २ [ARS] - -2 13 1 - 19 43 Apply (Ale -e 13-19 REA) 3 ID Appey Ra - 4 R2 trh R3 - 4 R3 +34 0 -13 Rj R3+5R2 RCAIR) 4 O o 521-52 here RCA) = REAIS Number of unknowns so system has inique solution

We can write equations from the marrux ans - 4x + 2y +z -2y+122 19 - est 52z = -52 er From ea Z = 52 - Substitute Z=1 in -24+13 E-1 =-19 -24 = 79 +13 -24 Substitute y, z calies in -42+213) + (-1) = 1 - 4x+6-7 = 1 -42=1-5 - 4x = 4 xz| (x, y, z) = (1, 3,-1) to option-2 correct