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Lesson Worksheet: Eigenvalues and Eigenvectors Mathematics

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=1337.

Q2:

Calculate the eigenvalues of the matrix 𝐴=111201223.

  • A1, 3, and 3
  • B3, 1, and 2
  • C1, 3, and 3
  • D1, 2, and 3
  • E1 and 2

Q3:

Calculate the eigenvalues of the matrix 𝐴=4125.

  • A3 and 6
  • B92+3172 and 92+3172
  • C3 and 6
  • D923172 and 92+3172
  • E9272𝑖 and 92+72𝑖

Q4:

Consider the matrix 𝐴=112121011.

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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