Determinant of a matrix.

For this course, we shall restrict ourselves to the determinant of a 2x 2 matrices only.

Definition:
The determinant of a 2 2 matrix is the difference between the products of the leading diagonal and the minor diagonal.
It is denoted as det.

Consider the matrix below:

image 83

Its determinant is denoted by det A or IAI and is defined as:

image 84

a) Given that

image 85

Solution

image 86

b) Given that A = PB. Find det A, if

image 87

Solution

image 88

c) Given that

image 89

possible values of a

Solution

image 90

Note:
Some matrices have det = 0. Such matrices are called singular matrices where as those for which det ≠0 are known as non-singular
matrices.