Finding the determinant of a 2 × 2 matrix
- Let’s calculate the determinant of the matrix A.
\[\Large
A =
\begin{bmatrix}
a & b \\
c & d
\end{bmatrix}
\]
- The determinant of the 2 × 2 matrix A can be calculated using the following formula.
\[\Large
A =
\begin{bmatrix}
\color{red}{a} & \color{blue}{b} \\
\color{orange}{c} & \color{purple}{d}
\end{bmatrix}
\]
\[\Large det(A) = \textcolor{red}{a}\textcolor{purple}{d~} – \textcolor{blue}{~b}\textcolor{orange}{c} \]
\[\Large det(A) = \textcolor{red}{a}\textcolor{purple}{d~} – \textcolor{blue}{~b}\textcolor{orange}{c} \]
\[\Large
\textbf{det(A) = ad – bc}
\]
- By solving the above formula, you can easily get the determinant of a 2 × 2 matrix.
Example:
\[\Large
A =
\begin{bmatrix}
\color{red}{2} & \color{blue}{3} \\
\color{orange}{4} & \color{purple}{5}
\end{bmatrix}
\]
\[\Large det(A) = \textcolor{red}{2} × \textcolor{purple}{5~} – \textcolor{blue}{~3} × \textcolor{orange}{4} \] \[\Large det(A) = 10~-~12 \]
\[\Large det(A) = -2 \]
\[\Large det(A) = \textcolor{red}{2} × \textcolor{purple}{5~} – \textcolor{blue}{~3} × \textcolor{orange}{4} \] \[\Large det(A) = 10~-~12 \]
\[\Large det(A) = -2 \]
What is the correct formula used to compute the determinant of a 2 × 2 matrix?