SOLUTION: Please someone help me! I have to put this in rref and I can't seem to figure out how! I just keep going around in circles! x-y+z=-3 x+y+z=-9 x+y-z=1

Question 79477: Please someone help me! I have to put this in rref and I can't seem to figure out how! I just keep going around in circles!

x-y+z=-3
x+y+z=-9
x+y-z=1
Answer by chitra(359) (Show Source): You can put this solution on YOUR website!
This is a very simple problem and the solution of this goes this way.

The given set of equations are:

x - y + z = -3
x + y + z = -9
x + y - z = 1

Hence, the augmented Matrix is given by:

[ 1 -1 1 -3 ]
[ 1 1 1 -9 ]
[ 1 1 -1 1 ]

Now to reduce the given matrix using Row Reduced Echelon form, the steps are as follows.
We perform only row operations to reduce to rref.

Now we perform the row operations. [ R1, R2, and R3 represents the row]

R2 - R1 and R3 - R1

[ 1 -1 1 -3 ]
[ 0 2 0 -6 ]
[ 0 2 -2 4 ]

We now divide the 2nd row by 2 and the third row by 3

That is R2/2 and R3/2

[ 1 -1 1 -3 ]
[ 0 1 0 -3 ]
[ 0 1 -1 2 ]

We now perfom the final row operation to eliminate one more variable.

That is R3 - R2 , Hence we get:

[ 1 -1 1 -3 ]
[ 0 1 0 -3 ]
[ 0 0 -1 5 ]

HEnce, the augmented matrix now reduces to:

x - y + z = -3 --------->(EQN 1)

y = -3 ------------> (EQN 2)

-z = 5 ------------> (EQN 3)

Hence, from equation (3) the value of "z" is:

==> z = -5

Hence, from equation (2) the value of "y" is:

==> y = -3

Thus, substituting for the values of y and z in equation (1), we find the "x" value.

x - y + z = -3

x - (-3) - 5 = -3

x + 3 - 5 = -3

x - 2 = -3

x = -3 + 2

x = -1

Hence, according to RREF, the values of x, y and z are:

x = -1 , y = -3, z = -5

Thus, the solution.

If you have any doubts you can get back to me ...

I'll surley help you.. :))

Regards,
Chitra
Online Math tutor
Knowledge Online Services
www.knowledgeonlineservices.com

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