Determinant of a Matrix in Matlab

In this lesson, I will explain how to compute the determinant of a square matrix using Matlab.

What is the determinant? The determinant of a square matrix is a scalar value that encapsulates the properties of the matrix. There are various methods for calculating the determinant, such as the straightforward formula for 2x2 matrices: $$ \det \begin{pmatrix} a & b \\ c & d \end{pmatrix} = a \cdot d - b \cdot c$$

Let's go through a practical example

Define a square 2x2 matrix and store it in the variable M

>> M = [ 1 5 ; 3 2 ]
M =

1 5
3 2

M is a square matrix with two rows and two columns, represented as:

$$ M = \begin{pmatrix} 1 & 5 \\ 3 & 2 \end{pmatrix} $$

Use the det() function in Matlab to calculate the determinant of matrix M

>> det(M)
ans = -13

The det() function returns the determinant of a square matrix, which in this case is -13.

Verification: To confirm the correctness of the result, manually calculate the determinant: $$ \det(M) = \det \begin{pmatrix} 1 & 5 \\ 3 & 2 \end{pmatrix} = 1 \cdot 2 - 5 \cdot 3 = -13 $$ The result matches, confirming the correctness of the computed determinant.