Question

3. Solve the following systems of equations using Gaussian elimination. (a) 2x 3x2 + 2x3 = 0 (d) 2x + 4x2 2.xz 4 *- x2 + x3 = 7 X; - 2x2 · 4x3 = -1 -X, + 5x2 + 4x3 = 4 - 2x - X2 3x3 = -4

Answer 1

(3) 2) 22 322 +223 - 0 34 22 tag 7 4 hus .x+502 +4&z System of equation in matriz form 2 2 94 0 7 X2 م -1 4 5 4 Its augmented matrix is, 2 - 3 2 0 - 1 7 - -1 5 4 4 -1 7 0 52 ist ] - 3 2 3. (swap the and and ist rows - 1 5 4 4 multiply 2 the est now by a 2 14 2 -2 2 -3 -1 5 2 4 4

2 -2 14 -14 Ro'= R₂-RI - 1 > - 1 4 " — -1 7 7 -14 REL -1 5 4 4 v iT 7. -14 R3 R3 tR, 0 o 4 5 > 21 Ri=RI-R2 Ri's - 1 -14 " 5 11 - 0 2 l -14 Rog Roz t4R2 UT O O -45 21 R2 = (-1) R2 0 14 -45 5 21 > R3 1 / 3 R3 o q - 30 Ri'= R, -R3 14 оо o Hene ai given, 215 30 062 14 23 E-9

3) (d) 2x + 482 - 2x3 = 4 4 - 222 – 423 - 224 -X2 - 3X3 - 4 system af equation in matrix form, 2 4 :4 -2 -2 -4 :)) -2 -3 its augmented inted matrix matrix is , 2 4 - 2 - 2 -4 -3-4 -2 -2 -4 a a s - 1 4 swap the 1st 2 1st and -2 2nd nows -2 -3 -4 -2 4 -1 Re' - R2 2 Ri 0 8 6 no - 2 - 3 -4 hale - - 2 4 I R3 + 2 RI V 0 Rg 8 6 6 0 -5 -Il -6 - 2 -4 3/4 Ry's BR 0 3/4 o -5 0 -52 Y2 → Ri'- Ri + 2 R2 0 314 314 -- 5 -U - 6

- 5% 3/4 / 3/4 -914 Ro'= R3 +5R2 0 -2974 - 0 Y2 V -572 314 314 Rg'= 1 R. 14 29 ) R3 balb 37/29 Ri'= Rit to jest R3 - 314 3/4 9/29 个 37/29 15/29 9/29 Re' = R9 - RS o - Hene given 24 = 37/29 15/29 X2 = 23 9/29