Suppose A is a symmetric 3 × 3 matrix with eigenvalues λ 1 , λ 2 , and λ 3 , with |λ 3 | 2 | 1 |. Suppose the starting vector for the power method contains a portion of an eigenvector for λ 1 . Write...

Suppose
A
is a symmetric 3 × 3 matrix with eigenvalues λ₁, λ₂, and λ₃, with |λ₃|
₂|
₁|. Suppose the starting vector for the power method contains a portion of an eigenvector for λ₁. Write out what happens to (4.12) and (4.13) in this 3 × 3 case. Also, what happens to the error (4.15) and the iterative error (4.16) formulas?