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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^2c2  c 1 c  cb  With my answer that if (c2)(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 (c2)(c+1) cb (c2)(c+1)=0 when c=2 or c=1 and cb=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 
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 . Since is invertible, the solution is . This is just a simple matrix multiplication. 

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matrix, reduction, row, unknown, values 
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