Math Is Fun Forum

mrpace

Member

Registered: 2012-08-16

Posts: 88

How do i find this simple determinent?

Matrix P =

              0  0  0  1
              0  0  1  0
              0  1  0  0
              1  0  0  0

Can I just assume that the det=1 because it's just a re-arrangment of the identity matrix? Or does the mix up of order affect the determinent? thanks.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: How do i find this simple determinent?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,441

Website

Re: How do i find this simple determinent?

Can I just assume that the det=1 because it's just a re-arrangment of the identity matrix? Or does the mix up of order affect the determinent? thanks.

The determinant is indeed 1, but you must be careful. Here are some rules about how row (or column) operations affect the determinant of a matrix.

Let the matrix B be obtained from the matrix A by applying the row operation e. Then:

.

These results hold true for the corresponding column operations.

For your matrix, the identity matrix has had two row operations: P(1,4) and P(2,3). So the determinant of your new matrix is (-1)*(-1)*1 = 1.