Determinant Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Find detโก[5234]\det\begin{bmatrix} 5 & 2 \\ 3 & 4 \end{bmatrix}.

Solution

  1. 1
    detโก=5(4)โˆ’2(3)=20โˆ’6=14\det = 5(4) - 2(3) = 20 - 6 = 14.
  2. 2
    Since detโก=14โ‰ 0\det = 14 \neq 0, the matrix is invertible.

Answer

1414
Apply adโˆ’bcad - bc directly. The sign of the determinant indicates orientation (positive = same, negative = flipped), and its absolute value gives the area scaling factor.

About Determinant

The determinant is a scalar value computed from a square matrix that encodes important geometric and algebraic information. For a 2ร—22 \times 2 matrix [abcd]\begin{bmatrix} a & b \\ c & d \end{bmatrix}, the determinant is adโˆ’bcad - bc. A nonzero determinant means the matrix is invertible.

Learn more about Determinant โ†’

More Determinant Examples

Example 1 easy

Find [formula].

Example 2 hard

Evaluate [formula] by expanding along the first row.

Example 4 medium

Is [formula] invertible?

โ† All Determinant Examples Determinant Concept