Evaluate the determinant of a specific 3x3 matrix using cofactor expansion.

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Evaluate a 3x3 Determinant

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Evaluate the determinant \begin{vmatrix} 1 & -2 & -1 \\ 3 & 2 & -3 \\ 1 & 5 & 4 \end{vmatrix}.

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What you need first

Basic arithmetic with negative numbers
The definition of a determinant for a 2x2 matrix

What this problem tests

Tests the ability to correctly apply the formula for a 3x3 determinant and perform basic arithmetic operations with careful attention to signs.

Evaluating 3x3 determinants is a fundamental skill in linear algebra and multivariable calculus, often used for finding cross products, volumes, and solving systems of equations.

Evaluate a 3x3 Determinant

What you need first

What this problem tests

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