What are some examples of determinants in mathematics?

What are some examples of determinants in mathematics?

Determinants are used in linear algebra to determine properties of matrices. For example, the determinant of a 2x2 matrix ( \begin{pmatrix} a & b \ c & d \end{pmatrix} ) is calculated as ( ad - bc ). Would you like to see more examples?

Yes, can you show me a 3x3 matrix example?

Sure! For a 3x3 matrix ( \begin{pmatrix} a & b & c \ d & e & f \ g & h & i \end{pmatrix} ), the determinant is calculated as ( a(ei - fh) - b(di - fg) + c(dh - eg) ). Would you like to know how to apply this?

How do I apply this determinant in solving linear equations?

Determinants can help determine if a system of linear equations has a unique solution. If the determinant of the coefficient matrix is non-zero, the system has a unique solution. Would you like to see an example of this?