Question

UseGauss-Jordan method to solve the following system of linear equations 2x – 3y + z = 0 5x + 4y + z = 10 2x – 2y – z = -1

Answer 1

22-3y + z = 0 5x+4y+z=10 2x-2y- Z = -1 From the expressed systens given above, it can be [mateix equation, as AX = В 2 - 3 10 ។ oi Z 2 2-1 Х А To apply Gauss- Joedan Method considee the Augmented mateix [A, B] 2 - 3 Ra → Ri-Rog 4 - 2 R2 ya Ra d to o סרי) -1 2!! O 2 - 3 1 RRI-R 2 4 ulos 51 211 다. 2 -23 1-4 3 - -3 llo do R3 R₂ + 23 Rp. 1211 -23 31-4 51

2-310 -1 211 TO R3---3 R3 0 0 -431-43 s -3 Ilo -12 O Til is dark [A (13] = Rank(A) = 3.: The system consistent and since the binobee of variables is equal to the eark. It has a conique solution. becomes fean the seduced systems -3 2 0 X -U ។ 2 Z = 1 Y+22= 1 = -y= 1-2 y = 1 2x-3y + z = 0 → 2X = 3y-Z → 2X = 3-1 X = 1 x= 1, y = 1, Z=1