3×3 matrix determinant calculator (LaTeX style)

3×3 matrix determinant

Let \[ A = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix}\]

the determinant can be computed by Laplace expansion along any row or column. Using the first row:

\[ \det(A) = a \cdot \det\begin{bmatrix}e&f\\h&i\end{bmatrix} - b \cdot \det\begin{bmatrix}d&f\\g&i\end{bmatrix} + c \cdot \det\begin{bmatrix}d&e\\g&h\end{bmatrix} \]

which simplifies to:

\[ \det(A) = a(ei - fh) - b(di - fg) + c(dh - eg) \]
given 3×3 matrix
\[ A = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} \]

\(\det \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix}\)

row‑1 expansion: a(ei - fh) - b(di - fg) + c(dh - eg)

\(\text{entries } \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix}\)
row 1
row 2
row 3
\(\text{precision}\)

result in decimal format (fractions evaluated).

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