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5. Compute the characteristic polynomial, (ii) the eigenvalues; (iii) a basis for each eigenspace, and (iv , the algebraic and geometric multiplicities for each of ...

Question

5. Compute the characteristic polynomial, (ii) the eigenvalues; (iii) a basis for each eigenspace, and (iv , the algebraic and geometric multiplicities for each of the following matrices (a)A =0[3 0 55 00 1 2 0B

5. Compute the characteristic polynomial, (ii) the eigenvalues; (iii) a basis for each eigenspace, and (iv , the algebraic and geometric multiplicities for each of the following matrices (a) A = 0 [3 0 55 0 0 1 2 0 B



Answers

Find the geometric and algebraic multiplicity of each eigenvalue of the matrix $A$, and determine whether $A$ is diagonalizable. If $A$ is diagonalizable, then find a matrix $P$ that diagonalizes $A,$ and find $P^{-1} A P.$ $$A=\left[\begin{array}{lll}5 & 0 & 0 \\1 & 5 & 0 \\0 & 1 & 5\end{array}\right]$$


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