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December 8th, 2013, 08:16 AM  #1 
Newbie Joined: Dec 2013 Posts: 2 Thanks: 0  Why Isn't This Matrix Invertible?
I need to show this matrix isn't invertible, but I'm not seeing why. 0 a 0 0 0 b 0 c 0 0 0 d 0 e 0 0 0 f 0 g 0 0 0 h 0 
December 8th, 2013, 09:24 AM  #2 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: Why Isn't This Matrix Invertible?
The middle row is a linear combination of the first and the last.

December 11th, 2013, 02:09 AM  #3 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Why Isn't This Matrix Invertible?
Another approach would be to show the determinant is zero. Expand along the top row. Now we need to find that 4x4 determinant , expand along the second row. Now that 3x3 determinant is 0 because it has a row of 0's , so det(A) = (a)(e)(0) = 0 Therefore the matrix A is not invertible. 

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