My Math Forum Matrix row reduction with unknown values

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 January 23rd, 2011, 10:39 PM #1 Newbie   Joined: Aug 2008 Posts: 13 Thanks: 0 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.
 January 24th, 2011, 02:20 AM #2 Senior Member   Joined: Nov 2010 From: Staten Island, NY Posts: 152 Thanks: 0 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 $c\ne 2$ and $c\ne 1$ There are infinitely many solutions if $b=c=2$ or $b=c=-1$ There is no solution if $c=2$ or $-1$, but $b\ne c$
 January 24th, 2011, 02:30 AM #3 Newbie   Joined: Aug 2008 Posts: 13 Thanks: 0 Re: Matrix row reduction with unknown values yes thank you, this is what the question is.
 January 24th, 2011, 07:16 AM #4 Newbie   Joined: Aug 2008 Posts: 13 Thanks: 0 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.
 January 24th, 2011, 07:40 AM #5 Newbie   Joined: Aug 2008 Posts: 13 Thanks: 0 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
 January 24th, 2011, 09:43 AM #6 Senior Member   Joined: Nov 2010 From: Staten Island, NY Posts: 152 Thanks: 0 Re: Matrix row reduction with unknown values I think that the question you are asking is to solve the matrix equation $AX=B$. Since $A$ is invertible, the solution is $X=A^{-1}B$. This is just a simple matrix multiplication.

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# how to find the value of unknown in matrices

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