13.14: Matrix Determinant

Fundamentals of MATLAB Programming · LibreTexts

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    From LibreTexts, under CC BY-NC-SA, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    The determinant of a square matrix is a single number that gives important information about the matrix. In MATLAB, the determinant is calculated using the det function.

    For example:

    Example \(\PageIndex{1}\)
    A = [2 1; 4 3];
detA = det(A)
    Solution

    detA = (2 * 3) - (4 * 1) = 2

    The determinant is only defined for square matrices, meaning matrices with the same number of rows and columns.

    What Does the Determinant Tell Us?

    One of the most important uses of the determinant is determining whether a square matrix has an inverse.

    If the determinant is not zero, the matrix is invertible.

    If the determinant is zero, the matrix is singular, which means it does not have an inverse.

    For example:

    A = [2 1; 4 3];
det(A)

    returns a nonzero value, so matrix A is invertible.

    But:

    B = [1 2; 2 4];
det(B)

    returns 0, so matrix B is singular. Notice that the second row of B is just two times the first row. This means the rows are not independent.

    This page titled 13.14: Matrix Determinant was last modified on Tue, 30 Jun 2026 02:11:59 GMT and is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Zara Noroozi.