What is the determinant of a matrix and how do I calculate it?

What is the determinant of a matrix and how do I calculate it?

The determinant is a scalar value that can be computed from the elements of a square matrix. It provides important information about the matrix, such as whether it is invertible.

Can you show me how to calculate the determinant of a 2x2 matrix?

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

What about a 3x3 matrix?

For a 3x3 matrix [ B = \begin{pmatrix} a & b & c \ d & e & f \ g & h & i \end{pmatrix} ] the determinant can be calculated using the formula: ( \text{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 does not have an inverse.