Find all matrices for which is an eigenvector with associated eigenvalue 5.
So, the required matrix is .
Eigenvector: An eigenvector of A is a nonzero vector v in such that , for some scalar .
If is an Eigen vector of A this means that:
Now let , and .
We want to solve for A.
To do this we will replace everything into the equation and we will have:
b,d are any real number
Thus, all matrices of the form will satisfy the given requirements.
For a given eigenvalue, find a basis of the associated eigensspace .use the geometric multiplicities of the eigenvalues to determine whether a matrix is diagonalizable.
For each of the matrices A in Exercise 1 through 20 ,find all (real)eigenvalues.Then find a basis of each eigenspaces,and diagonalize A, if you can. Do not use technology.
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