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Chapter 7: Q46E (page 325)
If is an eigenvector of matrix A with associated eigenvalue 3 , show that is an image of matrix A .
Hence is an image of A .
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Arguing geometrically, find all eigenvectors and eigenvalues of the linear transformations in Exercises 15 through 22. In each case, find an eigenbasis if you can, and thus determine whether the given transformation is diagonalizable.
Reflection about a plane v in.
Find all the polynomials of degree [a polynomial of the form] whose graph goes through the points (1,3) and (2,6) , such thatrole="math" localid="1659541039431" [wheredenotes the derivative].
Consider the linear space of allmatrices for which all the vectorsare eigenvectors. Describe the space(the matrices in"have a name"), and determine the dimension of.
find an eigenbasis for the given matrice and diagonalize:
Show that similar matrices have the same eigenvalues. Hint: Ifis an eigenvector of, thenrole="math" localid="1659529994406" is an eigenvector of A.
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