What is the determinant of a matrix?

What is the determinant of a matrix?

The determinant is a scalar value that can be computed from the elements of a square matrix. It provides important properties about the matrix.

How do I calculate the determinant of a 2x2 matrix?

For a 2x2 matrix, say ( A = \begin{pmatrix} a & b \ c & d \end{pmatrix} ), the determinant is calculated as ( det(A) = ad - bc ).

Can you give me an example of a 3x3 matrix and its determinant?

Sure! For a 3x3 matrix ( B = \begin{pmatrix} a & b & c \ d & e & f \ g & h & i \end{pmatrix} ), the determinant is ( det(B) = a(ei - fh) - b(di - fg) + c(dh - eg) ).

What does the determinant tell us about the matrix?

The determinant indicates whether the matrix is invertible. If the determinant is zero, the matrix is singular and not invertible.