Solving for 2 systems at once

• Apr 5th 2011, 06:26 AM
DrZ
Solving for 2 systems at once
I dont think I understand what this question is asking, if someone could explain what it means with its explanation it would help a lot.

solve the 2 systems

x1 + 2x2 - 2x3 =1 x1 + 2x2 - 2x3 = 9
2x1 + 5x2 +x3 = 9 2x1 + 5x2 +x3 = 9
x1 + 3x2 + 4x3 = 9 x1 + 3x2 + 4x3 = -2

the question gives this explanation

by doing elimination on a 3x5 augmented matrix and the performing two back substitutions.

I thought it meant to put the two systems together, but since the 2nd row of equations are the same there would only be 5, not 6 I would use so it would be 3x5.

1 2 -2 1
2 5 1 9
1 3 4 9
1 2 -2 9
1 3 4 -2

but then that would make 2 rows
0 0 0 x
and then wouldn't it be inconsistent. But the book has answers to the question so its not that. What is this question even asking me to do?
• Apr 5th 2011, 07:58 AM
Ackbeet
It's asking you to solve two systems that happen to have the same coefficient matrices, but different RHS's. So take the augmented matrix suggested, namely,

$\left[
\begin{array}{rrr|rr}
1 &2 &-2 &1 &9\\
2 &5 &1 &9 &9\\
1 &3 &4 &9 &-2
\end{array}
\right],$

and perform ero's on it in order to make it upper triangular. (Usual Gaussian elimination.) What do you get?
• Apr 5th 2011, 01:24 PM
DrZ
thanks. weird the textbook does not show any matrices with the 2 right columns at all in the first section where the question came from.

I ended up getting it triangular and getting the right answers for each system.
• Apr 5th 2011, 01:32 PM
Ackbeet
Quote:

Originally Posted by DrZ
thanks. weird the textbook does not show any matrices with the 2 right columns at all in the first section where the question came from.

I ended up getting it triangular and getting the right answers for each system.

Excellent!