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January 23rd, 2011, 11:39 PM   #1
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Matrix row reduction with unknown values

Hi I have this question

for what values of 'c' does this system of equations not have a unique solution:

A =
0 1 1
c 0 2
1 1 c

and

B=
1
b
2

I have put this into the Augmented matrix AIB:
| 0 1 1 | 1 0 0 | 1 |
| c 0 2 | 0 1 0 | b |
| 1 1 c | 0 0 1 | 2 |

and done row reduction.

I ended up with the last line reading:

|0 0 c^2-c-2 | -c -1 c | c-b |

With my answer that if (c-2)(c+1) = 0, i.e. if c=2 or -1 the system does not have a unique solution as the system will have a row of 0's.

Can any1 check this for me please. Thanks.
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January 24th, 2011, 03:20 AM   #2
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Re: Matrix row reduction with unknown values

Your question doesn't make it clear what the system of equations is. I'm guessing it's the following:

y+z=1
cx+2z=b
x+y+cz=2

If this is the case, then you want to row reduce

0 1 1 1
c 0 2 b
1 1 c 2

I'm not sure why you attached the identity matrix.

The final row of your matrix is ok, but you haven't interpreted the information quite correctly:
The last row looks like this:

0 0 (c-2)(c+1) c-b

(c-2)(c+1)=0 when c=2 or c=-1 and c-b=0 when c=b

So, there is a unique solution as long as and

There are infinitely many solutions if or

There is no solution if or , but
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January 24th, 2011, 03:30 AM   #3
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Re: Matrix row reduction with unknown values

yes thank you, this is what the question is.
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January 24th, 2011, 08:16 AM   #4
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Re: Matrix row reduction with unknown values

can sum help me find the inverse of A if c=0, and also the solution X.

I dont know how to do this because the question states that c=0, but does not indicate what 'b' is.
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January 24th, 2011, 08:40 AM   #5
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Re: Matrix row reduction with unknown values

ok i found the inverse of A is

-1 1/2 1
1 -1/2 0
0 1/2 0

but I dont know how to find the solution X
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January 24th, 2011, 10:43 AM   #6
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Re: Matrix row reduction with unknown values

I think that the question you are asking is to solve the matrix equation .

Since is invertible, the solution is .

This is just a simple matrix multiplication.
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