A matrix has characteristic polynomial p(X) = (A + 4) (A + 9)³. Fill in the blanks with the best answer for each of the statements below. The dimension of the eigenspace corresponding to the eigenvalue -4 is necessarily ? ✓ The dimension of the eigenspace corresponding to the eigenvalue -9 is necessarily ? ✓ If the matrix is not diagonalizable, then the dimension of the eigenspace corresponding to the eigenvalue -9 is necessarily ? ✓ If the matrix is symmetric, then the dimension of the eigenspace corresponding to the eigenvalue -9 is necessarily ? ✓

Q: Calculate the characteristic polynomial of the following matrix A, and use it to compute eigenvalues…

A: We find characteristic polynomial and eigenvalues of A.

Q: _nteger?)

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A: Here given matrix as C=-2261-2-4-113

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A: We will show counterexample if the statement is false and will prove if the statement is true.

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A: "As per the rules, we are supposed to answer the first question and rest of the questions can be…

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