Hello, luxdelux!
Here's something that obviously didn't occur to you.
I'm not laughing at you ... It took me a long time to realize this.
We can re-order the equations: .
We have: .
. .
. .
. .
Therefore: .
Hi again, I'm not sure if it's okay for me to post in here again, as I posted last night--but this is truly urgent. I'll be taking a midterm in a short while and there are several questions on my study guide that have me completely stumped:
1. y + z = 2
x + y + z = -1
-x + z = -1
I have done this problem again and again, only to end up with different/wrong answers for x, y, and z each time. I know that I have to created an augmented matrix, so I did that, and then I continued to row reduce until I got the identity matrix on my left, and the the supposed (yet incorrect) solutions on the right. I don't know what I'm doing wrong here, and I'm beyond frustrated.
2. 2y + z = 0
y + z = 1
x - y = -1
Same situation here. I created the augmented matrix and then, when I saw that column one is [0 0 1], I don't know what to do.
3. -x + y +2z = 1
2x -2z = 0
2x + y + 2z = 0
I switched the first and second row here, then divided the first row by 2, and proceeded to use G-J, but messed up my calculations because I'm not getting the correct solutions for x, y, and z...I've re-done over and over and I'm not sure what I'm doing incorrectly.
4. 2x + y - z = 0
-x + y = 1
2x + y + 2z = 0
Same situation here...I've done the problem repeatedly only to end up with different x, y and z each time.
5. Suppose a two by two matrix A is nonsingular and is defined as follows:
A = ( a b
0 d ) < The whole thing is supposed to be in the parenthesis
where a, b, d are real numbers. Use Gauss-Jordan to find the inverse of A.
Again...I am at a total loss here. I think that I have to put an identity matrix in there somewhere?
I'd really appreciate the help on this...I have no idea what I'm doing, and I'm definitely panicking. THANK YOU!