Question

19 110 a 3 68. 3 bla 168a. a 39. C 3구 19a. 5 110.2 2135.구 aa4. 14.12 643.04 9ㅋ54.46 3552-28 i119.66 3 68.3 귀구. 구8 구68.43 2135.7 11863.2 3a643.S 3725.66 귀155. 45 63a구.26 1275,42 1190.구니 3 552. 28 19구5구.9 54154.9 6 la 11963.a 0980. 2 3509. 45 3281. 35 3a643.5 54154.9 149303 1683.a 9754.46 니D0.38 구구. as 83.42 구68.43 1245.42 3509.45 39-6 373.83 구ㅋ.25 190.구4 3281.35 구구. 구8 214.12 3구

Solve the matrix by Gauss-Jordan elimination method. Show ALL steps with formulas.
Ans:
X1= 3.122
X2= 0.644
X3= -0.009
X4= 0.504
X5= -0.119
X6= -2.465
X7= 1.505

Answer 1

Given, 19 110.2 368.3 612 1682.2 39.6 37 192.5 110.2 642.04 2135.7 3552.28 9754.46 229.52 214.12 1119.66 368.3 2135.7 7155.45 11863.2 32643.5 768.43 717.78 3725.66 612 3552.28 11863.2 19757.9 54154.9 1275.42 1190.74 6227.26 1682.2 9754.46 32643.5 54154.9 149323 3509.45 3281.35 16980.2 39.6 229.52 768.43 1275.42 3509.45 82.72 77.25 400.38 37 214.12 717.78 1190.74 3281.35 77.25 72.58373.83 R2=R2-(110.2/19)*R1 R3=R3-(368.3/19)*R1 R4=R4-(612/19)*R1 R5=R5-(1682.2/19) *R1 R6=R6-(39.6/19)*R1 R7=R7-(37/19)*R1

19 0 0 0 0 0 0 110.2 368.3 612 1682.2 39.6 37| 192.5 2 .88 -0.44 2.68 -2.3 -0.16 -0.48 3.16 -0.44 16.24526 0.063158 35.38105 0.815263 0.564211-5.80053 2.68 0.063158 45.05789 -29.6474 -0.11684 -1.04947 26.73368 -2.3 35.38105 -29.6474 386.3242 3.391053 5.486842-63.1421 -0.16 0.815263 -0.11684 3.391053 0.185263 0.134211 -0.83053 -0.48 0.564211 -1.04947 5.486842 0.134211 0.527368 -1.03842 R3=R3-(-0.44/2.88)*R2 R4=R4-2.68/2.88)*R2 R5=R5--2.3/2.88)*R2 RE=R6-(-0.16/2.88)*R2 R7=R7-(-0.48/2.88) *R2

19 0 0 0 110.2 368.3 612 1682.2 39.6 37| 192.5 2 .88 -0.44 2.68 -2.3 -0.16 -0.48 3.16 0 16.17804 0.472602 35.02966 0.790819 0.490877 -5.31775 0 0.472602 42.56401 -27.5071 0.032047 -0.60281 23.79313 0 35.02966 -27.5071 384.4874 3.263275 5.103509 |-60.6185 0 0.790819 0.032047 3.263275 0.176374 0.107544 -0.65497 0 0.490877 -0.60281 5.103509 0.107544 0.447368 -0.51175 0 R4=R4-0.472602/16.17804)*R3 R5=R5-(35.02966/16.17804)*R3 R6=R6-(0.790819/16.17804)*R3 R7=R7-(0.490877/16.17804)*R3 19 0 110.2 368.3 612 1682.2 39.6 37| 192.5 2 .88 -0.44 2.68 -2.3 -0.16 -0.48 3.16 0 16.31249 0.472602 35.73244 0.839708 0.637544 -5.31775 0 42.5502 -28.5304 0.008945 -0.61715 23.94847 0 -28.5304 308.6391 1.550947 4.040632-49.1042 0 0.008945 1.550947 0.137717 0.083549 -0.39503 0 -0.61715 4.040632 0.083549 0.432474 -0.3504

R5=R5--28.5304/42.5502) *R4 R6=R6-(0.008945/42.5502)*R4 R7=R7-(-0.61715/42.5502)*R4 19 0 0 2 110.2 368.3 612 1682.2 39.6 37| 192.5 .88 -0.44 2.68 -2.3 -0.16 -0.48 3.16 0 16.31249 0.472602 35.73244 0.839708 0.637544-5.31775 0 42.55031 -28.5423 0.007719 -0.62128 23.94719 0 289.5091 1.556944 3.626828 -33.0465 0 1.556944 0.137715 0.083678 -0.40006 0 3.626828 0.083678 0.423523 -0.00305

R6=R8(1556944/2895091)*R5 R7=R7-(3.626828/2895091)*R5 .19 _0 110.2 _368.3 _62_1682.2 _39.6 _37|_192.5_ _2.88 -044 _268 -23 -0.16 -0.48 | _3.16 ._0 16.31249 0.472602 35.73244 0.839708 0.637544|5.31775 0 42.55031 -28.5423 0.007719 -0.6212823.94719 . _0 288.6228 1.465249 3.317988| -33.147 _0 _0 _0 0 0.129342 0.0641747-0.22234 _0 _0 0 0.054174 0.378088|0,410936 _0 R7=R7-(0.064174/0.129342)*R6 [19 110.2 _368.3 _612 1682.2 _39.6 _37|_192.5 _0 _2.88 -0,44 _268 -23 -0.16 -0.48| _3.16 ._0 16.31249 0.472602 3573244 0.839708 0.6375445.31775 0 42.55031 .28.5423 0.007719 -0.62128 |23.94719 . _0 288.6228 1.465249 3.317988 | -33.147 _0_0.127861 0.059099 l-0.22578 0 0.346248 0.521251 _0 0

Now, 0.346248*X7=0.521251 Thus, X7=1.50542 Also, 0.127861*X6+0.059099*X7=-0.22578 Thus, X6=-2.4616 Also 288.6228*X5+1.465249*X6+3.317988*X7=-33.147 Thus, X5=-0.119 Also, 42.55031*X4-28.5432*X5+0.007719*X6-0.62128*X7=23.94719 Thus, X4=0.505

Also 16.31249*X3 +0.472602*X4 +35.73244*X5 +0.839708*X6 +0.637544*X7=-5.31775 Thus, X3=-0.009 = -0.01 Also, 2.88*X2 +0.44*X3+2.68*X4-2.3*X5-0.16*X6-0.48*X7=3.16 Thus, X2= 0.647 And, 19*X1+110.2*X2+368.2*X3+612*X4+168 2.2*X5+39.6*X6+37*X7=192.5 Thus, X1= 3.022

Hence, X1 = 3.022 X2 = 0.647 X3 = -0.009 0.505 X5 = -0.119 X6 = -2.4616 X7 = 1.50542