Question: need help with linear Algebra 1 0 1 (1) Consider the matrix A = 0 1 1 . 0 O 2 (a) Determine the eigenvalues

need help with linear Algebra

1 0 1 (1) Consider the matrix A = 0 1 1 . 0 O 2 (a) Determine the eigenvalues of A. (b) Find a basis of each eigenspace of A. Describe the eigenspaces geometrically. (c) Find three eigenvectors of A that are linearly independent. (Do they form a basis of IR3?) Let V1, V2, V3 be the three linearly independent eigenvectors you found in part (c), with v1 and v2 corresponding to the eigenvalue 1. (d) Let k E N. What is A*v? What is A*v2? What is Akv3? (e) Suppose v = C1V1 + C2V2 + C3V3. Express Av as a linear combination of V1, V2, V3. (Hint: Recall that Av = 1AV1 + C2Av2 + C3Av3)

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