# Matrices and parameters

1. Oct 23, 2008

### Gramsci

1. The problem statement, all variables and given/known data
Decide c, so that A(2)X=b(c) where

x=(x,y,z) and b(c)=(1,c,1)
A(2) is calculated from the previous problem:

"Decide the value on the parameter b so that the following system has solutions

(2, 1,-1,b
1, 2, 2, 2b
1,-1,-3, b+1)

2. Relevant equations

3. The attempt at a solution
Alright, I solved the previous problem that is stated and I got the answer to be b=-1/2
but from that, what do I do? The real question is, what does A(2)x mean? I substitute b for 2?

/Magnus

2. Oct 23, 2008

### Staff: Mentor

There seems to be some information missing. You mentioned a matrix A(2), but didn't show what it is.

You listed something else, namely
(2, 1,-1,b
1, 2, 2, 2b
1,-1,-3, b+1)
without explaining what it is.

What exactly is the problem you're trying to solve?

3. Oct 23, 2008

### Gramsci

The matrix A(2) is calculated from that one.
"decide the number c so that A(2)x=b(c)
where:
x= (x,y,z) and b(c)=(1,c,1)

A(2) is calculated from the previous example."
The previous example is:
Determine the value on the parameter b so that the following system has solutions:
(2, 1,-1,b
1, 2, 2, 2b
1,-1,-3, b+1)
Where this represents a 3x3 matrix. Any ideas?

4. Oct 23, 2008

### Staff: Mentor

By "that one" I assume you mean this 3 x 3 matrix (shown by rows):
{(2 1 -1), (1 2 2), (1 -1 -3)}

and
So, to summarize, A(2) is not shown and no description on how to get it is shown, and you don't know what it means.

Not much to go on...

5. Oct 23, 2008

### Gramsci

I'm sorry, it's probably my bad english that confuses you. A(2) is calculated from that 3x3 matrix yes, and I have no idea how to get it either. Do you have any idea?

6. Oct 23, 2008

### Gramsci

A 3x3 augmented matrix where the bs are the parameters. Just to clarify.

7. Oct 25, 2008

### Gramsci

No ideas?

8. Oct 25, 2008

### HallsofIvy

Staff Emeritus
"Calculated from it" HOW? "Calculating" it from the previous problem doesn't make sense because the only question in that problem is determing b which is only in the right hand side of the equation, not the coefficient matrix. Do you mean that it is the matrix
$$\left[\begin{array}{ccc} 2 & 1 & -1\\ 1 & 2 & 2 \\ 1 & -1 & -3\end{array}\right]$$?

If so then the problem is to solve
$$\left[\begin{array}{ccc} 2 & 1 & -1\\ 1 & 2 & 2 \\ 1 & -1 & -3\end{array}\right]\left[\begin{array}{c} x \\ y \\ z\end{array}\right]= \left[\begin{array}{ccc} 1 \\ c \\ 1\end{array}\right]$$

Last edited: Oct 25, 2008