Eigenvalues and Eigenvectors MCQ | Linear Algebra for AI Multiple Choice Questions

Direction: Choose the correct option

What is an eigenvector of a matrix?

A. A vector that becomes zero

B. A random vector

C. A vector that does not change direction when multiplied by the matrix

D. A vector that becomes the identity

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For a matrix A, the equation Av = λv means:

A. v is eigenvalue

B. Both are eigenvalues

C. λ is eigenvector

D. v is an eigenvector, λ is eigenvalue

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What is the characteristic equation for finding eigenvalues?

A. det(A - λI) = 0

B. trace(A) = λ

C. det(A) = λ

D. det(A + λI) = 0

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For a diagonal matrix, the eigenvalues are:

A. Ones

B. The diagonal entries

C. Zeros

D. The off-diagonal entries

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The sum of eigenvalues equals:

A. Determinant of the matrix

B. Number of rows

C. Trace of the matrix

D. Rank of the matrix

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