3 × 3 3\times3 determinant

Algebra Level 3

1 433 2 5 2 / 3 4 0 2 0 = ? \large \begin{vmatrix} 1 & -433\quad & 2 \\ 5 & 2/3 & 4 \\ 0 & 2 & 0 \end{vmatrix} = \ ?


The answer is 12.

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1 solution

1 433 2 5 2 / 3 4 0 2 0 = 2 × 5 × 2 1 × 4 × 2 = 20 8 = 12 \begin{aligned} \begin{vmatrix} \color{#D61F06}{1} & -433 & \color{#3D99F6}{2} \\ \color{#3D99F6}{5} & 2/3 & \color{#D61F06}{4} \\ 0 & \color{#69047E}{2} & 0 \end{vmatrix} & = \color{#3D99F6}{2\times 5 \times 2} - \color{#D61F06}{1\times 4 \times 2} = 20 - 8 = \boxed{12} \end{aligned}

Note that the other diagonals are zero.

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