Question: Answer the following short answer questions justification wanted). If the information given is not enough to uniquely determine the answer, write undetermined. Let A be an \(\mathrm{n}\) by n matrix with eigenvalues (including multiplicities) $3,3,4,4,4$.

1. What is \(\mathrm{n}\) ?
2. The determinant of \(A\) is:
3. The coefficient of \(\lambda^{4}\) in the characteristic polynomial of \(A\) is:
4. The dimension of the row space of \(A\) is:
5. The eigenvalues of the matrix \(A^{2}\) of \(A\) are:
6. Is \(A\) invertible?
7. The dimension of the eigenspace of \(A\) for the eigenvalue 3 is:
8. Is A diagonalizable?

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