For each of the matrices in Exercises 1 through 13, find all real eigenvalues, with their algebraic multiplicities. Show your work. Do not use technology.
Since, given matrix is triangular its eigenvalues are the entries on the main diagonal.
Find eigenvalues using characteristic equation as:
Hence, the answer is:
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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