Consider the following. 4 05 A = 6-16 5 04 (a) Compute the characteristic polynomial of A. det(AAI) = 0 (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) 21 = has eigenspace span 12 = has eigenspace span - I t (smallest -value) 13 = has eigenspace span (largest A-value) (c) Compute the algebraic and geometric multiplicity of each eigenvalue. A₁ has algebraic multiplicity 12 has algebraic multiplicity 13 has algebraic multiplicity | and geometric multiplicity and geometric multiplicity and geometric multiplicity

Consider the following. (a) Compute the characteristic polynomial of A. det(A – \I) = A₁ = (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) 2₂ A = = 10 0 1 89 8 -1 0 8 ^3 = has eigenspace span -4) span has eigenspace ↓ 1 has eigenspace span ↓ ↑ (c) Compute the algebraic and geometric multiplicity of each eigenvalue. has algebraic multiplicity and geometric multiplicity λ₂ has algebraic multiplicity and geometric multiplicity 23 has algebraic multiplicity and geometric multiplicity (smallest λ-value) (largest λ-value)

What is the relationship between the characteristic polynomial and the eigenvalues of A?

Consider the following. (a) Compute the characteristic polynomial of A. det(A - AI) = -2³ +72² +172 +9 A₁ = A = (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) ^₂ = 4 05 6-1 6 5 04 23 = has eigenspace span has eigenspace span has eigenspace span ↓ 1 (c) Compute the algebraic and geometric multiplicity of each eigenvalue. A₁ has algebraic multiplicity and geometric multiplicity ₂ has algebraic multiplicity and geometric multiplicity 13 has algebraic multiplicity and geometric multiplicity (smallest λ-value) (largest λ-value)