Find a basis for the eigenspace of a associated with

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A = , λ = 3 13 15 10 12 0 . .
Find a basis for the eigenspace of A associated with the given eigenvalue λ . 4 . . . 1
5. –/4 pointsholtlinalg1 6.1.024.nva Consider the matrix A Find the characteristic polynomial for the matrix A . (Write your answer in terms of λ 6. –/5 pointsholtlinalg1 6.1.025.nva Consider the matrix A A = 3 12 1 4 . .) (No Response) Find the real eigenvalues for the matrix A . (Enter your answers as a comma-separated list.) λ = (No Response) Find a basis for each eigenspace for the matrix A . [-3;1] (smaller eigenvalue) [4;1] (larger eigenvalue) Solution or Explanation Characteristic polynomial: Eigenvalues: Eigenspace of so a basis for this eigenspace is Eigenspace of so a basis for this eigenspace is . det( A λ I 2 ) = det λ = det = λ 2 + 7 λ . 3 12 1 4 1 0 0 1 λ 3 12 1 λ 4 λ 2 + 7 λ = λ ( λ + 7 ) = 0 λ = 0 or λ = 7 . λ = 7 : A ( 7 ) I 2 = ~ , 4 12 1 3 4 12 0 0 . 3 1 λ = 0: A 0 I 2 = ~ , 3 12 1 4 3 12 0 0 . 4 1
Find the characteristic polynomial for the matrix A . (Write your answer in terms of λ .) (No Response) Find the real eigenvalues for the matrix A . (Enter your answers as a comma-separated list.) λ = (No Response) Find a basis for each eigenspace for the matrix A [0;0;1] (smallest eigenvalue) [0;4/3;1] [5;5;1] (largest eigenvalue) . Eigenspace of A = 4 0 0 1 3 0 2 3 1 ) 0 0 λ 1. : ,
so a basis for this eigenspace is Eigenspace of so a basis for this eigenspace is Eigenspace of so a basis for this eigenspace is . 0 1 4 3 λ = 4 : A 4 I 3 = ~ , 0 0 0 1 1 0 2 3 5 1 1 0 0 1 5 0 0 0 . 5 5 1 λ = 1: A ( 1) I 3 = ~ , 5 0 0 1 4 0 2 3 0 5 0 0 0 4 0 0 0 0 . 0 0 1

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