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November 27th, 2016, 11:57 AM   #1
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How do I find the determinant of this matrix?

I have the following matrix:
A - square matrix of n*n as follows:



I figured out that the determinant is $\displaystyle (-1)^n(n-1)$, but how do I prove it?
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November 27th, 2016, 02:59 PM   #2
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The matrix isn't here.
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November 27th, 2016, 10:11 PM   #3
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Sorry, bad upload.
This the matrix:
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November 27th, 2016, 11:02 PM   #4
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given an $n \times n$ matrix

the determinant appears to be $(-1)^{n-1} (n-1)$

now prove it using induction
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November 27th, 2016, 11:47 PM   #5
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I already know what the determinant is, I wrote it in the original post.
What I don't know is how to prove it.
I tried using induction ans it didn't work.
Any other suggestions?
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November 28th, 2016, 04:20 AM   #6
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Okay i know this is irrelevant and it might sound stupid but this question is driving me crazy,
If x=4 and y=−5 find y2(xy+18 )
can someone please help me and show me how to answer the question,
thanks!
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November 28th, 2016, 06:23 AM   #7
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Angry

Quote:
Originally Posted by Mathmonsters View Post
Okay i know this is irrelevant and it might sound stupid but this question is driving me crazy,
If x=4 and y=−5 find y2(xy+18 )
can someone please help me and show me how to answer the question,
thanks!
I don't understand how that has any connection to my question...
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