Note that 7 0 3 2 3 4 1 1 2 2 3 9 8 11 34 5 7 21 1 0 0 0 1

Note that [7 0 -3 2 3 4 1 -1 -2] [-2 3 9 8 -11 -34 -5 7 21] = [1 0 0 0 1 0 0 0 1] (You do not need to prove this.) Use this fact to solve 7x_1 + 2x_2 + x_3 = 21 3x_2 - x_3= 5 -3x_1 + 4x_2 - 2x_3 = -1 without using Gaussian elimination.

Solution

Your matrix

Make the pivot in the 1st column by dividing the 1st row by 7

Eliminate the 1st column

Make the pivot in the 2nd column by dividing the 2nd row by 3

Eliminate the 2nd column

Make the pivot in the 3rd column by dividing the 3rd row by 1/21

Eliminate the 3rd column

Solution set:

x1 = 3

x2 = 1

x3 = -2

	X1	X2	X3	b
1	7	2	1	21
2	0	3	-1	5
3	-3	4	-2	-1