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Lesson Worksheet: Eigenvalues and Eigenvectors Mathematics

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In this worksheet, we will practice finding the eigenvalues of a matrix and the corresponding eigenvectors of a matrix.

Q1:

Calculate the eigenvalues of the matrix 𝐴=1−337.

Q2:

Calculate the eigenvalues of the matrix 𝐴=11−120−1−223.

  • A1, 3, and 3
  • B−3, 1, and 2
  • C−1, −3, and 3
  • D−1, 2, and 3
  • E1 and 2

Q3:

Calculate the eigenvalues of the matrix 𝐴=4−1−25.

  • A−3 and −6
  • B−92+3√172 and −92+3√172
  • C3 and 6
  • D92−3√172 and 92+3√172
  • E92−√72𝑖 and 92+√72𝑖

Q4:

Consider the matrix 𝐴=11−2−12101−1.

Calculate the three eigenvalues 𝜆, 𝜆, and 𝜆 of 𝐴.

  • A𝜆=2, 𝜆=−1, and 𝜆=1
  • B𝜆=4, 𝜆=−2, and 𝜆=2
  • C𝜆=2, 𝜆=−2, and 𝜆=−1
  • D𝜆=2, 𝜆=−2, and 𝜆=1
  • E𝜆=−2, 𝜆=1, and 𝜆=−1

Which of the vectors 𝑣, 𝑣, and 𝑣 are corresponding eigenvectors for 𝜆, 𝜆, and 𝜆?

  • A𝑣=111, 𝑣=101, and 𝑣=221
  • B𝑣=111, 𝑣=101, and 𝑣=321
  • C𝑣=131, 𝑣=111, and 𝑣=321
  • D𝑣=131, 𝑣=101, and 𝑣=321
  • E𝑣=131, 𝑣=101, and 𝑣=221

This lesson includes 10 additional questions for subscribers.

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