Practice Determinant in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The determinant is a scalar value computed from a square matrix that encodes important geometric and algebraic information. For a 2 \times 2 matrix \begin{bmatrix} a & b \\ c & d \end{bmatrix}, the determinant is ad - bc. A nonzero determinant means the matrix is invertible.
The determinant measures how a matrix scales area (in 2D) or volume (in 3D). If \det(A) = 3, the transformation described by A triples all areas. If \det(A) = 0, the transformation collapses space into a lower dimension (like squishing a plane into a line), which is why the matrix has no inverse.
Example 1
easyFind \det\begin{bmatrix} 3 & 1 \\ 2 & 4 \end{bmatrix}.
Example 2
hardEvaluate \det\begin{bmatrix} 2 & 1 & 3 \\ 0 & -1 & 2 \\ 1 & 0 & 4 \end{bmatrix} by expanding along the first row.
Example 3
easyFind \det\begin{bmatrix} 5 & 2 \\ 3 & 4 \end{bmatrix}.
Example 4
mediumIs \begin{bmatrix} 2 & 4 \\ 1 & 2 \end{bmatrix} invertible?