Expansion by Minors

Date: 10/26/1999 at 23:22:26
From: Jessica Bullard
Subject: How to evaluate determinants using expansion by minors

How do you evaluate determinants using expansion by minors?

     |-3  0  6|
     | 6  5 -2|
     | 1  4  2|

That's the problem originally. I tried doing the "T" thing where you 
take the -3 and place it outside the absolute value things, then draw 
a line through the 0, 6 across from it and the 6, 1 below it. Then 
place the rest of the numbers inside the absolute value things in 
the order they are in, but I don't know what to do from there... I 
know the answer should be 60 but I can't get that answer - I keep 
getting -174.

Help me, please.

Date: 10/27/1999 at 08:32:57
From: Doctor Jerry
Subject: Re: How to evaluate determinants using expansion by minors

Hi Jessica,

It's best to use row operations first to produce more zeros, but you 
didn't mention that so I won't do it. Choose a column or row with the 
most zeros - the second column for example.

Then the determinant is

     d = 0*(-1)*m0 + 5(+1)*m1 + 4(-1)*m2

where

     m0 = |6  -2|
          |1   2|

        = 12 - (-2)

        = 14

          (We didn't need to compute this minor, since it'll be 
           multiplied by 0)

     m1 = |-3  6|
          | 1  2|

        = -6 - 6

        = -12

and

     m2 = |-3  6|
          | 6 -2|

        = 6 - 36

        = -30

So,

     d = 0*(-1)*m0 + 5(+1)*m1 + 4(-1)*m2

       = 0*(14) + 5(-12) - 4(-30)

       = 0 - 60 + 120

       = 60

- Doctor Jerry, The Math Forum
  http://mathforum.org/dr.math/