Matrix Determinants
1
Please read your test for the 3×3 instances. I cannot write it any better.
© Arizona State University, Department of Mathematics and Statistics
1 of
3
Objectives:
At the end of this lesson, you should be able to:
1.
Create a
matrix determinant
from a
system
or
matrix
.
2.
Calculate the determinant for 2×2
and
3×3 matrices
1
.
Background
By now I’m sure you know that matrices are not numbers. However there is a number associated with each
square matrix. It even has a use!
This number, called the
determinant,
has application in finding area, volumes and such in three dimensional
situations. Your text has both an explanation and examples of that. However, these are less useful for the
business world than in science. Nonetheless, finding a determinant is a skill the Business School wants you to
acquire.
Determinants Defined
We define the
determinant
of a 2×2 matrix
as the curiously crossed product
.
11
12
21
22
a
a
a
a
11
22
12
21
a a
a a

Our symbols for the
determinant
are
. It’s your choice.
11
12
21
22
det(
)
a
a
A
A
a
a
=
=
The symbol looks like an absolute value symbol, but in the context of a discussion, there should not be any
confusion. Also, please notice that
is an array of numbers, while
is definitely a number. Do not
11
12
21
22
a
a
a
a
11
12
21
22
a
a
a
a
intermix them! We have special vocabulary related to the value of the determinant.
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 Spring '12
 DavidGlenn
 Linear Algebra, Algebra, Determinant, Matrices, Invertible matrix, Cramer

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