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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. $det A \= \ \|0 \ a \ 0 \ 0 \ 0 \\ b \ 0 \ c \ 0 \ 0 \\ 0 \ d \ 0 \ e \ 0 \\ 0 \ 0 \ f \ 0 \ g \\ 0 \ 0 \ 0 \ h \ 0 \| \ = \ (-a) \cdot \|b \ c \ 0 \ 0 \\ 0 \ 0 \ e \ 0 \\ 0 \ f \ 0 \ g \\ 0 \ 0 \ h \ 0 \|$ Now we need to find that 4x4 determinant , expand along the second row. $(-a) \cdot (e) \cdot \| b \ c \ 0 \\ 0 \ f \ g \\ 0 \ 0 \ 0 \|$ 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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