As shown below, which are the following matrix A characteristic value? (Multiple choice)

Question

Options

• A2
• B-2
• C4
• D4

• A
  86% (31)
• B
  8% (3)
• C
  6% (2)

Explanation

Options A (2) and D (4) are the eigenvalues of matrix A because they satisfy the characteristic equation det(A − λI) = 0, meaning there exist non-zero vectors x such that Ax = λx for λ = 2 and λ = 4.

Option B (-2) is incorrect because the negative value −2 does not satisfy the characteristic equation for this matrix - a common trap since students sometimes confuse a negated eigenvalue with a valid one when working with sign errors during row reduction or determinant expansion.

Options C and D both show the value 4, which appears to be a transcription error in the problem (likely C was a different value such as −4 or 0); only D is marked correct, meaning whatever value C originally represented was not a root of the characteristic polynomial.

Memory tip: Eigenvalues are the roots of det(A − λI) = 0 - think of them as the values that "shrink" the determinant to zero. Always double-check signs when expanding the determinant, as sign errors are the most common reason students incorrectly select negative distractors like −2.

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