how to tell if determinant is negative or positve of 4x4 matrix

• November 9th 2007, 01:03 AM
lord12
how to tell if determinant is negative or positve of 4x4 matrix
2,3-1,1
-1,0,1,1
2,1,3,-2
1,1,1,-1

Is there any way of quickly determining this?
• November 9th 2007, 04:39 AM
TKHunny
No. Row reductions will tell you soon, but I wouldn't call it "quickly".
• November 9th 2007, 04:47 AM
kalagota
Quote:

Originally Posted by lord12
2,3-1,1
-1,0,1,1
2,1,3,-2
1,1,1,-1

Is there any way of quickly determining this?

use expansion method:

$det (A) = a_{i1}A_{i1} + a_{i2}A_{i2} + ... + a_{in}A_{in}$
this is expansion about the ith row..
• November 9th 2007, 04:50 AM
TKHunny
Also, "no". Certainly, it can be determined using a few methods.