Determinant Math Example 1

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

Example 1

easy
Find detโก[3124]\det\begin{bmatrix} 3 & 1 \\ 2 & 4 \end{bmatrix}.

Solution

  1. 1
    Step 1: Apply formula: detโก=adโˆ’bc\det = ad - bc where a=3,b=1,c=2,d=4a=3, b=1, c=2, d=4.
  2. 2
    Step 2: detโก=3(4)โˆ’1(2)=12โˆ’2=10\det = 3(4) - 1(2) = 12 - 2 = 10.
  3. 3
    Check: Since detโกโ‰ 0\det \neq 0, the matrix is invertible โœ“

Answer

1010
The 2ร—22 \times 2 determinant is computed as adโˆ’bcad - bc (product of main diagonal minus product of anti-diagonal). A nonzero determinant means the matrix is invertible.

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 2 hard

Evaluate [formula] by expanding along the first row.

Example 3 easy

Find [formula].

Example 4 medium

Is [formula] invertible?

โ† All Determinant Examples Determinant Concept