Determinant Math Example 4

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Example 4

medium
Is [2412]\begin{bmatrix} 2 & 4 \\ 1 & 2 \end{bmatrix} invertible?

Solution

  1. 1
    det⁡=2(2)−4(1)=4−4=0\det = 2(2) - 4(1) = 4 - 4 = 0.
  2. 2
    Since det⁡=0\det = 0, the matrix is singular (not invertible).

Answer

No, the determinant is 00.
A matrix is invertible if and only if its determinant is nonzero. This matrix is singular because row 1 is exactly twice row 2, making the rows linearly dependent.

About Determinant

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

Learn more about Determinant →

More Determinant Examples

Example 1 easy

Find [formula].

Example 2 hard

Evaluate [formula] by expanding along the first row.

Example 3 easy

Find [formula].

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