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Math Foundations
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Linear Algebra
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Eigenvalues & eigenvectors
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835.
Zero Eigenvalue Implications
medium
A matrix A has eigenvalue λ = 0 with a corresponding nonzero eigenvector v. What does this imply?
A
A is the zero matrix — all eigenvalues must be zero if any one eigenvalue is zero
B
A is singular — it maps v to the zero vector and cannot be inverted
C
A is the identity matrix — zero eigenvalues always accompany unit eigenvalues in square matrices
D
A is symmetric — only symmetric matrices can have zero as an eigenvalue
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