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Let \(A\) be a square matrix. Which of the following statement about eigenvectors is correct?

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If \[ \boxed{ A\mathbf{x}=\lambda\mathbf{x}, } \] then every non-zero scalar multiple \[ \boxed{ k\mathbf{x},\;k\neq0, } \] is also an eigenvector corresponding to the same eigenvalue.

Updated On: Jul 14, 2026

Eigen vectors are always unique
Eigen vectors are unique only if the eigen value has multiplicity \(1\)
Eigen vectors are unique up to a scalar multiple
Eigen vectors cannot be scaled

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The Correct Option is C

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The Correct Option is C

Solution and Explanation

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