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Eigenvalues and Eigenvectors (Linear Algebra)

Free printable university Linear Algebra worksheet on computing eigenvalues from the characteristic polynomial and finding eigenvectors of 2x2 and 3x3 matrices, with integer answers.

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Linear Algebra · Math worksheet
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Linear Algebra: Eigenvalues and Eigenvectors

Find all eigenvalues of each matrix from the characteristic polynomial det(A - λI) = 0, then find an eigenvector for each eigenvalue by solving (A - λI)v = 0. Eigenvectors are determined up to a non-zero scalar multiple. Matrices are written in row form, e.g. [1, 2; 3, 4]; column vectors as [1; 2].

  1. 1.
    Find the eigenvalues and corresponding eigenvectors of A = [20, -24; 16, -20].
  2. 2.
    Find the eigenvalues and corresponding eigenvectors of A = [-6, 3; -36, 15].
  3. 3.
    Find the eigenvalues and corresponding eigenvectors of A = [3, 6; 0, 5].
  4. 4.
    Find the eigenvalues and corresponding eigenvectors of A = [-12, -6; 36, 18].
  5. 5.
    Find the eigenvalues and corresponding eigenvectors of A = [-16, 6, -3; -58, 21, -10; 10, -4, 3].
  6. 6.
    Find the eigenvalues and corresponding eigenvectors of A = [2, 2, 2; 3, 3, -2; -6, -6, -1].
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