For the following matrix A: 4 0-2 A = 0 2 0 1 0 1 i....

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For the following matrix A: 4 0-2 A = 0 2 0 1 0 1 i. Calculate A 48 and A0, then comment on whether or not these vectors are eigenvectors of A. If they are, give the corresponding eigenvalues. ii. Find the characteristic equation using the form D(A)=b3A³ + b₂A² + b₁λ + bo and calculating the coefficients bo, b₁,b2, b3 using the formulas on page 17 of the study guide (Topic 6 and e.g., see online module 6.3. b₂ = -tr(A) in this case). iii. Now identify the characteristic equation D(X) in factorised form by first expanding the determinant |AI - A. (Hint: you should be able to factor out one of the (A-ai) factors first, and then expand and factorise the resulting quadratic equation) iv. Use the factorised form of D(X) to identify the eigenvalues of A, and then solve (XI-A)x = 0 to find all eigenvectors not identified in part (i). For the following matrix A: 4 0-2 A = 0 2 0 1 0 1 i. Calculate A 48 and A0, then comment on whether or not these vectors are eigenvectors of A. If they are, give the corresponding eigenvalues. ii. Find the characteristic equation using the form D(A)=b3A³ + b₂A² + b₁λ + bo and calculating the coefficients bo, b₁,b2, b3 using the formulas on page 17 of the study guide (Topic 6 and e.g., see online module 6.3. b₂ = -tr(A) in this case). iii. Now identify the characteristic equation D(X) in factorised form by first expanding the determinant |AI - A. (Hint: you should be able to factor out one of the (A-ai) factors first, and then expand and factorise the resulting quadratic equation) iv. Use the factorised form of D(X) to identify the eigenvalues of A, and then solve (XI-A)x = 0 to find all eigenvectors not identified in part (i).