Determinant is defined for square matrices. A square matrix has the same number of rows as columns, like a
matrix
or a
matrix
.
We will discuss few applications of determinant. The cross product of two vectors in can be defined using the determinant of a
matrix.
The area of the parallelogram generated by these two vectors can be be obtained using as a determinant.
The volume of the parallelepiped formed by any three nonzero vectors in
, also can be find using determinant.
Determinant is used in change of variable of integrals in calculus. It can be used in finding eigenvalues of matrix. Determinant of a matrix can tell us about invertible of the matrix, number of solutions of an a linear system of n-equations in n-unknowns, and many other applications.