What does the determinant of a matrix tell you?

The determinant of a square matrix is a single number that, among other things, can be related to the area or volume of a region. In particular, the determinant of a matrix reflects how the linear transformation associated with the matrix can scale or reflect objects.

How is the determinant related to linear transformations?

Such a linear transformation can be associated with an m×n matrix. One can calculate the determinant of such a square matrix, and such determinants are related to area or volume. It turns out that the determinant of a matrix tells us important geometrical properties of its associated linear transformation.

What happens if the determinant of a 2×2 matrix is 0?

When the determinant of a matrix is zero, the volume of the region with sides given by its columns or rows is zero, which means the matrix considered as a transformation takes the basis vectors into vectors that are linearly dependent and define 0 volume.

Are determinants the same as matrices?

Frequently Asked Questions on Determinants and Matrices The determinant is defined as a scalar value which is associated with the square matrix. If X is a matrix, then the determinant of a matrix is represented by |X| or det (X).

What does the determinant of a matrix tell you about finding inverse of matrix?

The inverse of a matrix exists if and only if the determinant is non-zero. You probably made a mistake somewhere when you applied Gauss-Jordan’s method. One of the defining property of the determinant function is that if the rows of a nxn matrix are not linearly independent, then its determinant has to equal zero.

What is the determinant of the inverse of a matrix?

The determinant of the inverse of an invertible matrix is the inverse of the determinant: det(A-1) = 1 / det(A) [6.2. 6, page 265]. Similar matrices have the same determinant; that is, if S is invertible and of the same size as A then det(S A S-1) = det(A).

How do you find the determinant and inverse of a 2×2 matrix?

To find the inverse of a 2×2 matrix: swap the positions of a and d, put negatives in front of b and c, and divide everything by the determinant (ad-bc).