What double augmented matrix should be used in elimination to solve both equations at once?
Solve both of these equations by working on a 2 by 4 Matrix:
1) | 1 4 | | x |....| 1 |
....| 2 7 | | y | = | 0 |
2) | 1 4 | | u |....| 0 |
....| 2 7 | | v | = | 1 |
Note: Both have the same matrix, A.
Also, don't mind the periods. I used them for the sake of formatting the matrices.
I don't get how the person came up with the EAx part from Yahoo Answers:
So the question asks you to combine both questions into a single 2x4 matrix, so it would look like:
|1 4 1 0| = Ax
|2 7 0 1|
Now you need to come up with an elimination matrix to solve for u, v, x, and y simultaneously. So first we will solve for the 2 bottom variables (y and v, respectively) first.
EAx = | 1 0| |1 4 1 0| = |1 4 1 0|
|-2 -1| |2 7 0 1| |0 1 2 -1|
This gives us y=2 and v=-1. Now we solve for the top variables (x and u).
|1 -4| |1 4 1 0| = |1 0 -7 4|
|0 1| |0 1 2 -1| |0 1 2 -1|
So now we have:
|x u| = |-7 4|
|y v| |2 -1|
However, the question asks what double augmented matrix we are using in elimination. To get our final answer, we simply multiply the two elimination matrixes we used together.
| 1 0| |1 -4| = | 1 -4|
|-2 -1| |0 1| |-2 -1|
I hope this helped
Any help would greatly be appreciated. Thanks.