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3. Let V be a vector space over C and let L: V→ V be a linear transformation. (a) Give the eigenval (b) Suppose that u EV is an eigenvector of L with eigenvalue A and wE V is an eigenvector of L with eigenvalue μ. If λ μ, prove that u + w is not an eigenvector of L. (c) For all C prove that To a subspace of v 12 0 (d) Now let A = - 02 1 Find the eigenvalues of A and for each eigenvalue find a 10-1 corresponding eigenvector.

3. Let V be a vector space over C and let L: V→ V be a linear transformation. (a) Give the eigenval (b) Suppose that u EV is an eigenvector of L with eigenvalue A and wE V is an eigenvector of L with eigenvalue μ. If λ μ, prove that u + w is not an eigenvector of L. (c) For all C prove that To a subspace of v 12 0 (d) Now let A = - 02 1 Find the eigenvalues of A and for each eigenvalue find a 10-1 corresponding eigenvector.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. Let V be a vector space over C and let L: V→ V be a linear transformation. (a) Give the ciconvalue of (b) Suppose that u € V is an eigenvector of L with eigenvalue X and w€ V is an eigenvector of L with eigenvalue μ. If X µ, prove that u + w is not an eigenvector of L. (c) For all C prove that = 12 0 02 1 Find the eigenvalues of A and for each eigenvalue find a 10-1 corresponding eigenvector. To a subspace or v (d) Now let A =
Transcribed Image Text:3. Let V be a vector space over C and let L: V→ V be a linear transformation. (a) Give the ciconvalue of (b) Suppose that u € V is an eigenvector of L with eigenvalue X and w€ V is an eigenvector of L with eigenvalue μ. If X µ, prove that u + w is not an eigenvector of L. (c) For all C prove that = 12 0 02 1 Find the eigenvalues of A and for each eigenvalue find a 10-1 corresponding eigenvector. To a subspace or v (d) Now let A =
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