Worksheet: Eigenvectors of a Matrix

In this worksheet, we will practice determining the linearly independent eigenvectors of a nonzero square matrix associated with the eigenvalues of the matrix.

Q1:

Suppose one eigenvalue of a real matrix is and the corresponding eigenvector is Which of the following must also be an eigenpair of ?

  • A and
  • B and
  • C and
  • D and

Q2:

Suppose that 𝑣 is an eigenvector of a matrix 𝐴 corresponding to a nonzero eigenvalue 𝜆 . Is 𝐴 𝑥 = 𝑣 always solvable?

  • AYes
  • BNo

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