Solution Found!
Let u be an eigenvector of A corresponding to an
Chapter , Problem 11E(choose chapter or problem)
Let u be an eigenvector of A corresponding to an eigenvalue \(\lambda\), and let H be the line in \(\mathbb{R}^n\) through u and the origin.
a. Explain why H is invariant under A in the sense that Ax is in H whenever x is in H.
b. Let K be a one-dimensional subspace of \(\mathbb{R}^n\) that is invariant under A. Explain why K contains an eigenvector of A.
Questions & Answers
QUESTION:
Let u be an eigenvector of A corresponding to an eigenvalue \(\lambda\), and let H be the line in \(\mathbb{R}^n\) through u and the origin.
a. Explain why H is invariant under A in the sense that Ax is in H whenever x is in H.
b. Let K be a one-dimensional subspace of \(\mathbb{R}^n\) that is invariant under A. Explain why K contains an eigenvector of A.
ANSWER:Solution 11E(a), , we have , so by the definition o