5. [20 points] You are given that the eigenvalues of $A = \begin{bmatrix} 1 \\ 0 \end{bmatrix} \begin{bmatrix} 4 \\ 2 \end{bmatrix}$ are 1 and 2. Is A diagonalizable? If so, find matrices $P$ and $D$ such that $A = PDP^{-1}$ where $D$ is diagonal.
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Since the eigenvalues of A are 1 and 2, we need to determine the multiplicity of each eigenvalue. However, the problem statement does not provide this information. Without knowing the multiplicity of each eigenvalue, we cannot determine if A is diagonalizable. Show more…
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