CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 8. Systems and Matrices

8.7 Determinant of Matrices

Here you will find the determinants of 2×2 and higher order matrices.
Adeterminantis a number computed from the entries in a square matrix. It has many properties and interpretations
that you will explore in linear algebra. This concept is focused on the procedure of calculating determinants. Once
you know how to calculate the determinant of a 2×2 matrix, then you will be able to calculate the determinant of a
3 ×3matrix. Once you know how to calculate the determinant of a 3×3 matrix you can calculate the determinant
of a 4×4 and so on.
A logical question about determinants is where does the procedure come from? Why are determinants defined in
the way that they are?

Watch This

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/61650

http://www.youtube.com/watch?v=OI07C1HsOuc James Sousa: Determinants

Guidance

The determinant of a matrixAis written as|A|. For a 2×2 matrixA, the value is calculated as:

A=

[a b

c d

]

detA=|A|=

∣∣

∣∣a bc d

∣∣

∣∣=ad−bc

Notice how the diagonals are multiplied and then subtracted.
The determinant of a 3×3 matrix is more involved.

B=





a b c

d e f

g h i





Usually you will start by looking at the top row, although any row or column will work. Then use the checkerboard
pattern for signs (shown below) and create smaller 2×2 matrices.



+ − +

− + −

+ − +



