Determinants

Summary

• The determinant of a \(2×2\) matrix

\[A=\begin{bmatrix}a & b\\c & d\end{bmatrix}\]

• is denoted by \(|A|\) or \(det(A)\) and it is defined as the real number

\[\left| A \right|=ad-cb\]

• The determinant for a square \(n×n\) matrix \(A\) , \(|A|\) or \(det(A)\) , is also a real number (exactly how it is calculated is not part of this lecture).
• If \(A\) is not a square matrix, it has no det erminant.
• Result: A square \(n×n\) matrix \(A\) is invertible if and only if \(|A|≠0\) .