Question: 3 24 (2) The matrix A 202 4 2 3 has a characteristic equation of (A-8)(A+1)=0. (a) What are the algebraic multiplicities of the

3 24 (2) The matrix A 202 4 2 3 has a

3 24 (2) The matrix A 202 4 2 3 has a characteristic equation of (A-8)(A+1)=0. (a) What are the algebraic multiplicities of the eigenvalues of A? 10 -1 (b) The RREF of the matrix A-SI is 0 1 -1/2 00 0 How many free variables does the solution set for (A-8)=0 have? (c) How many linearly independent eigenvectors are there for the eigenvalue A = 8? 1 1/2 1 (d) The RREF of the matrix A+I is 00 0 0 0 0 How many free variables does the solution set for (A + 1) = 0 have? (e) How many linearly independent eigenvectors are there for the eigenvalue A = -1? (f) What is the geometric multiplicity of the eigenvalue A = 8? (g) What is the geometric multiplicity of the eigenvalue = -1? (h) Is the matrix A diagonalizable?

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