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### 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.

```

```
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/
```
Associated Topics:
College Linear Algebra
High School Linear Algebra

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