Determinant of a matrix in Octave

In this tutorial, we'll be exploring how to calculate the determinant of a matrix using Octave.

What is the determinant of a matrix? The determinant is a specialized scalar value that encapsulates certain properties of a matrix. Notably, it can only be computed for square matrices. For instance, the determinant of a 2x2 matrix can be calculated using the following formula: $$ \det \begin{pmatrix} a & b \\ c & d \end{pmatrix} = a \cdot d - b \cdot c$$

Let's examine this through a practical example.

Firstly, create a 2x2 square matrix, assigning it to the variable M:

>> M = [ 2 7 ; 1 5 ]
M =

2 7
1 5

This creates a square matrix M with two rows and two columns.

$$ M = \begin{pmatrix} 2 & 7 \\ 1 & 5 \end{pmatrix} $$

To calculate the determinant of this matrix, use the det(M) function at the command line:

>> det(M)
ans = 3

The det() function calculates and displays the determinant of a square matrix.

In this case, the determinant of the matrix is 3.

Verifiy. Let's verify this. Here's the step-by-step method on how you can manually compute the determinant of a matrix: $$ \det(M) = \det \begin{pmatrix} 2 & 7 \\ 1 & 5 \end{pmatrix} = 2 \cdot 5 - 7 \cdot 1 = 10 - 7 = 3 $$ As you can see, the result is correct.