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 Post subject: Find this determinantPosted: Thu, 13 Nov 2008 08:01:17 UTC
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Joined: Sun, 23 Mar 2008 10:55:47 UTC
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Find the determinant of the matrix

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 Post subject: Posted: Thu, 13 Nov 2008 20:45:05 UTC
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Joined: Mon, 10 Jan 2005 18:23:46 UTC
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Using a for alpha, if if ,otherwise:

From each row of A, subtract the row directly below to get:

Now starting with row 1 to row (n-1) successively replace Row n with:

to get:

Now det(A)=det(B)=det(C)=product of diagonal elements of C :

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 Post subject: Posted: Thu, 13 Nov 2008 22:35:51 UTC
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Joined: Mon, 10 Jan 2005 18:23:46 UTC
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Location: baltimore, md
An Inductive derivation might be as follows:

robbwrr wrote:
Using a for alpha, if if ,otherwise:

From each row of A, subtract the row directly below to get:

Spoiler:
Expanding by minors (column 1)

In 2d determinant, successively subtract each row from the row above it:

And now:

and then using the above:

follows.

Or a faster direct way, finally noticed this morning:

Spoiler:
Subtracting rows then subtracting columns :

These have the same determinant and expanding by the 1st column:

since each minor is all zeros either above or below the main diagonal.

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