031 Review Part 3, Problem 3

Let  $A={\begin{bmatrix}5&1\\0&5\end{bmatrix}}.$

(a) Find a basis for the eigenspace(s) of  $A.$

(b) Is the matrix  $A$  diagonalizable? Explain.

Foundations:
Recall:
1. The eigenvalues of a triangular matrix are the entries on the diagonal.
2. By the Diagonalization Theorem, an  $n\times n$  matrix  $A$  is diagonalizable
if and only if  $A$  has  $n$  linearly independent eigenvectors.

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

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