Calculating determinants is one of the most important operations in linear algebra. Therefore, given the importance of this mathematical procedure, we have decided to create the online Determinant Calculator that we offer to you completely free of charge.
To calculate the determinant of a matrix with this calculator, you only need to follow three simple steps:
The solution is explained step by step using four different methods: the triangle rule, Sarrus’s rule, Cofactor expansion, and Gaussian elimination method.
Remember that the matrix must be square to calculate its determinant.
The concept of determinant can be understood as a function that takes a square matrix as input and returns a number as output. It is important to remember that a square matrix has the same number of rows as it has columns. The determinant of a matrix can also be defined as a scalar property of the matrix. Determinants are very useful in mathematics since they allow us to determine if a matrix is invertible or not, solve systems of simultaneous linear equations using Cramer’s rule, find the area of triangles if the coordinates of their vertices are known, and many other applications. There are several notations to refer to the calculation of determinants, such as the abbreviation “det” followed by the matrix, or the matrix enclosed between two vertical bars, which should not be confused with the absolute value of a matrix.
Given the 2×2 matrix
We have that its determinant is equal to the product of the elements of the main diagonal minus the product of the elements of the secondary diagonal.
To find the determinant of a 3×3 matrix, we first need to perform some multiplication operations. For each element in the first row, we multiply that element by the determinant of the 2×2 matrix that is formed by removing the row and column of that element. This is called the “cofactor method.” Here’s the formula: