Definition of determinants
CraigsMaths
Mathematics Teaching for Learning
Determinants, Engineering Maths B
July 30th, 2008 by Craig Rose
Permalink: http://www.craigsmaths.com/ea003-engineering-mathematics-b/definition-of-determinants/
Determinants are only defined for square matrices. This article states the formulae for a 2×2 matrix, a 3×3 matrix and the general case. The general case is used when finding determinants of 4×4 matrices or bigger and most often when solving simultaneous equations. These large matrices involve quite a deal of computation and in real world situations would usually be solved by computers.
The determinant of a 2×2 matrix
2x2 Matrix
Determinant
The determinant of a 3×3 matrix
3x3 Matrix
Determinant
The determinant of an nxn matrix
For a fixed row i:
Determinant of A by columns
or for a fixed column j:
Determinant of A by rows
Where:
Cofactor of A
and where is the minor of
formed by excluding row i and column j
Hint: When choosing the fixed row (i) or fixed column (j) choose one with the most zeros in it.
