# Matrices and parameters

## Homework Statement

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)

## 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

Mark44
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?

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?

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?

Mark44
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)}

The matrix A(2) is calculated from that one.
and
A(2) is calculated from the previous example.

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...

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...
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?

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

No ideas?

HallsofIvy
$$\left[\begin{array}{ccc} 2 & 1 & -1\\ 1 & 2 & 2 \\ 1 & -1 & -3\end{array}\right]$$?
$$\left[\begin{array}{ccc} 2 & 1 & -1\\ 1 & 2 & 2 \\ 1 & -1 & -3\end{array}\right]\left[\begin{array}{c} x \\ y \\ z\end{array}\right]= \left[\begin{array}{ccc} 1 \\ c \\ 1\end{array}\right]$$