Table of Contents
Formulas for Determinants of Matrices
Determinant of a 2 by 2 Matrix
Let A be 2 by 2 matrix
\( A = \begin{bmatrix}
a_1 & a_2 \\
b_1 & b_2 \\
\end{bmatrix} \)
The determinant of matrix \( A \) is denoted by \( |A| \) and given by
\( |A| = \begin{vmatrix}
a_1 & a_2 \\
b_1 & b_2 \\
\end{vmatrix} = a_1 b_2 - a_2 b_1 \)
Determinant of a 3 by 3 Matrix
Let a 3 by 3 matrix \( A \) given by
\( A = \begin{bmatrix}
a_1 & a_2 & a_3\\
b_1 & b_2 & b_3 \\
c_1 & c_2 & c_3 \\
\end{bmatrix} \)
The determinant of matrix \( A \) is given by
\( |A| = \begin{vmatrix}
a_1 & a_2 & a_3\\
b_1 & b_2 & b_3 \\
c_1 & c_2 & c_3 \\
\end{vmatrix} = a_1 \begin{vmatrix}
b_2 & b_3 \\
c_2 & c_3 \\
\end{vmatrix} - a_2 \begin{vmatrix}
b_1 & b_3 \\
c_1 & c_3 \\
\end{vmatrix} + a_3 \begin{vmatrix}
b_1 & b_2 \\
c_1 & c_2 \\
\end{vmatrix} \)
There are many other forms for the determinant of \( n \times n \) matrices for \( n \gt 2 \).
More References and Links
Handbook of Mathematical Functions
Engineering Mathematics with Examples and Solutions