SOLUTION: [1 2 -1 | 5] [0 1 -2 | 1] [0 1 0 | 0] Answer(3-3z, 1+2z, z) and [1 2 1 | -3 ] [0 1 -3 | -1/2] [0 0 0 | 4 ] Answer(No Solutions) I know the answers but I would

Algebra ->  Matrices-and-determiminant -> SOLUTION: [1 2 -1 | 5] [0 1 -2 | 1] [0 1 0 | 0] Answer(3-3z, 1+2z, z) and [1 2 1 | -3 ] [0 1 -3 | -1/2] [0 0 0 | 4 ] Answer(No Solutions) I know the answers but I would       Log On


   

Question 1131187: [1 2 -1 | 5]
[0 1 -2 | 1]
[0 1 0 | 0]
Answer(3-3z, 1+2z, z)
and
[1 2 1 | -3 ]
[0 1 -3 | -1/2]
[0 0 0 | 4 ]
Answer(No Solutions)
I know the answers but I would like to know how to get them as well.
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

First write down the augmented matrix and begin Gauss-Jordan elimination:

Your matrix:
matrix%283%2C4%2C1%2C+2%2C+-1%2C+5%2C0+%2C1%2C+-2+%2C+1%2C0+%2C1%2C+0+%2C+0%29

Find the pivot in the 1st column in the 1st row:


Find the pivot in the 2nd column in the 2nd row:


Eliminate the 2nd column:


Make the pivot in the 3rd column by dividing the 3rd row by 2:


Eliminate the 3rd column:


Solution set:
x+=+9%2F2
y+=+0
z+=+-1%2F2
check your answer: Answer(3-3z,+1%2B2z, z)
x=3-3z=3-3%28-1%2F2%29=3%2B3%2F2=6%2F2%2B3%2F2=9%2F2
y=1%2B2z=1%2B2%28-1%2F2%29=1-1=0
(3-3z,+1%2B2z, z) =(9%2F2,+0, -1%2F2)


Your matrix:
matrix%283%2C4%2C1%2C+2%2C+1%2C-3%2C0+%2C1%2C+-3+%2C+-1%2F2%2C0+%2C0%2C+0+%2C+4%29

Find the pivot in the 1st column in the 1st row:


Find the pivot in the 2nd column in the 2nd row:


Eliminate the 2nd column:


Solution set:
The system is inconsistent
The system of equations corresponding to this REF has as its third equation
0%2Ax+%2B+0%2Ay+%2B+0%2Az+=4
This equation clearly has no solutions - no assignment of numerical values to x, y and+z will make the value of the expression 0%2Ax+%2B+0%2Ay+%2B+0%2Az equal to anything but zero. Hence the system has no solutions.