Determinant of a Matrix (2x2)

Determinant of a Matrix (2x2)

How to find the determinant of a matrix (2x2): formula, examples, and their solutions.

Formula

The determinant of a 2x2 matrix is ad - bc. It determines the properties of a matrix.

For a 2×2 matrix [a b / c d],
the determinant of the matrix is
|a b / c d| = ad - bc.

It determines the properties of a matrix.

One of the properties
that the determinant of a matrix determines
is to see if the matrix has an inverse matrix.

Example 1

Find the determinant of [1 2 / 3 4].

|1 2 / 3 4| = 1⋅4 - 2⋅3 = -2.

Example 2

Find the value of x. det[2 7 / 3 x] = 5.

det[2 7 / 3 x] is another way
to write the determinant of [2 7 / 3 x].

So |2 7 / 3 x| = 2x - 7⋅3.

It says det[2 7 / 3 x] = 5.

So |2 7 / 3 x| = 2x - 7⋅3 = 2x - 21 = 5.