Question

Please help me

tise the 12 6 3 -6 Gauss- Jordan : -8 6 101, 34 -2 2 4 !12 -13 9 3 127 4 1-18 (-38

Answer 1

The Augmented Matrix is 512 -8 6 10 1 341 6 -2 2 4 1 12 3 -13 9 3 27 (-6 4 1 -18 | -38] For Gauss - Jordan Method, we need to reduce 4x4 matrix on left side of line to Identity matrix. We need to perform elimination on rows first The row operations should be done on both sides simultaneously. Pivots on each step are highlighted which should be used to reduce rows below. Perform the following row operations: R2 -> R2 R1 R3 R4 -> -> R3 R4 - + R2 R1 512 0 0 LO -8 2 -11 0 6 -1 7.5 4 10 -1 0.5 -13 | 34 1 -5 18.5 -21] Perform the following row operations: R3 -> R3 + R2 512 10 0 10 -8 2 0 0 6 -1 2 4 10 -1 -5 -13 34 1 -5 -9 -21 Perform the following row operations: R4 -> R4 - R3 512 0 0 10 -8 2 0 0 6 -1 2 0 10 -1 -5 --- übü

Now, we have reduce the matrix to row-echelon form. Now, all the pivots (The diagonal elements of left side) should be equal to 1. So perform the following row operations. R1 -> R1/12 R2/2 R3/2 R4/(-3) 11 10 Jo LO -2/3 1 0 0 0.5 -0.5 1 0 5/6 -0.5 -2.5 1 | 17/61 -2.5 -4.5 1 1 Now, we need to reduce elements above diagonal elements to 0. Perform the following row operations: R1 -> R1 + R2 | 11 0 0 LO 0 1 0 0 1/6 -0.5 1 0 0.5 -0.5 -2.5 1 7/61 -2.5 -4.5 1 ] Perform the following row operations: R1 -> R1 - R3 R2 -> R2 + R3 11 0 0 0 1 0 O 0 1 LO 0 0 11/12 | 23/121 -1.75 -4.75 -2.5 -4.5 1 L 1 ] Perform the following row operations: R1 -> R1 - R4 R2 R3 -> -> R2 R3 + + 1.75 R4 2.5 R4

F1 0 0 [0 0 1 0 0 0 0 1 0 0 0 0 1 | | | 1 1] -3| -2] 1 ] Thus, the solution vector is 14