Math Is Fun Forum

nashfire

Member

Registered: 2008-03-19

Posts: 1

matrix

hi every1...
help me...
hw cn we find the det of a 4X4 matrix

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: matrix

expand it into 4 3x3 determinents along a row or collumn, this is a general method of finding a determinent

i.e. for a 4x4 you can have:

notice that each 'minor' matrix is obtained by deleting the row and collumn associated with the entry.

the pattern of +/- is found with the table

i.e. when the addition of the entry numbers is even, you have a plus, when odd you have a minus.

if you allow minor matrix at i,j to be

then you have the cofactor

hence the determinent of the 4x4 matrix above can be written as

and in general for an NxN matrix you have via a row.

or via collumn

Last edited by luca-deltodesco (2008-03-19 06:13:49)

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: matrix

In general, it's quite a lot of work to find the determinant of a 4x4 matrix. But as luca said, you can choose any row or column to calculate the determinant with, so if you pick a row or column that has a lot of zero entries then you'll cut down on the work a bit.

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nashfire

Member

Registered: 2008-03-19

Posts: 1

Re: matrix

hi.. help me ...
prove square root of 3 is irrational
thanks

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: matrix

Here is a proof that √2 is irrational. You can prove your statement in a similar way.

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