Question

Find the solution set of the system of linear equations represented by the augmented matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set

x4 = t

and solve for x1, x2, and x3 in terms of t.)

leftbracket4.gif 1 2 0 1 4
rightbracket4.gif
0 1 2 1 5
0 0 1 2 2
0 0 0 1 4
(x1, x2, x3, x4) = ( )

Answer 1

The system has unique solution.

Using backward substitution we have

1.
`x_4=4`

2.

`x_3+2x_4=2\\x_3+2(4)=2\\x_3+8=2\\x_3=-6`

3.

`x_2+2x_3+x_4=5\\x_2+2(-6)+4=5\\x_2-12+4=5\\x_2=5+8\\x_2=13`

4.

`x_1+2x_2+x_4=4\\x_1+2(13)+4=4\\x_1+26+4=4\\x_1=-26`

The the solution is
`(x_1,x_2,x_3,x_4)=(-26,13,-6,4)`