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HW 9: Eigenvalues & Eigenvectors -- Problem 4 of 12
Score so far: 3/3 correct
Find all eigenvalues of the matrix A. Then find the corresponding eigenvectors.
A = [ 3 1 ]
[ 1 3 ]
[ 1 3 ]
Enter eigenvalues (separate with commas):
Enter eigenvector for lambda = 4 (as a column vector):
Enter eigenvector for lambda = 2:
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Eigenvalues correct!
The eigenvalues lambda = 4 and lambda = 2 are correct. These were found by solving det(A - lambda*I) = 0, which gives (3-lambda)^2 - 1 = 0, yielding lambda^2 - 6*lambda + 8 = 0.
det(A - lambda*I) = (3-lambda)^2 - 1 = lambda^2 - 6*lambda + 8 = (lambda-4)(lambda-2) = 0
All Assignments
HW 9: Eigenvalues & Eigenvectors
3/12
Due TueHW 8: Diagonalization
92%
92%HW 7: Determinants
88%
88%HW 6: Subspaces & Basis
95%
95%Midterm 2: Chapters 4-6
94%
94%HW 5: Linear Transformations
90%
90%