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johnnyBravo

How is this basic 2x2 matrix calculated?

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Hi, I'm doing co-factors in matrices, and one of the steps involved this: So how does this:
Quote:
Come to this:
Quote:
eg for the first one: this 2x2 matrix |2 -3| |1 5| = 13 What calculations are involved? and is the (-1)^2 multiplied against that equation after or before that calculation eg do you work out a value from the 2x2 matrix and then multiply with (-1)^2 or you somehow multiply (-1)^2 with it first? Thanks

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The bars mean determinant (the brackets are a matrix), and for a 2x2 it looks like this:

|a b| = ad - bc
|c d|

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Oh thats what it means, i took a guess that might be what i meant earlier, so i tried getting the determinate equation off the net and it gave me this:
link
Quote:

Determinant
Every square matrix M has a number associated with it called its determinant and denoted by |M|. The determinant describes the volume of certain geometric shapes and provides information concerning the effect that a linear transformation has on areas and volumes of objects.
For a 2x2 matrix the determinant is simply the difference of two products.

This is the difference of the cross products.



Weird anyway.

Thanks alot

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