Question

using gauss -jordan method solve the system2x+y+z=10,3x+2y+3z=18,x+2y+9z=16

Answer 1

Multiply equation (C) by 2 (D) 2x + 4y - 6z = 2 Add eq. (D) term by term to eq. (A) (A) -2x + 3y + z = 3 (D) 2x + 4y - 6z = 2 ------------------------- (E) 7y - 5z = 5 Multiply equation (C) by -3 (F) -3x - 6y + 9z = -3 Add eq. (F) term by term to eq. (B) (B) 3x - y + 2z = 2 (F) -3x - 6y + 9z = -3 --------------------------- (G) -7y + 11z = -1 Add eq. (G) term by term to eq. (E) (E) 7y - 5z = 5 (G) -7y + 11z = -1 --------------------------- 6z = 4 z = 6/4 z = 3/2 Multiply eq. (E) by 11 (H) 77y - 55z = 55 Multiply eq. (G) by 5 (I) -35y + 55z = -5 Add eq. (I) term by term to eq. (H) (H) 77y - 55z = 55 (I) -35y + 55z = -5 --------------------------- 42y = 50 y = 50/42 y = 25/21 ------------------------------------- (A) -2x + 3y + z = 3 (B) 3x - y + 2z = 2 (C) x + 2y - 3z = 1 Multiply equation (B) by 3 (J) 9x - 3y + 6z = 6 Add eq. (J) term by term to eq. (A) (A) -2x + 3y + z = 3 (J) 9x - 3y + 6z = 6 ------------------------- (K) 7x + 7z = 9 Multiply equation (B) by 2 (L) 6x - 2y + 4z = 4 Add eq. (L) term by term to eq. (C)