The symmetric matrix                                 has eigenvectors x 1 = (1, −2) T and x 2 = (−2, 1) T . (a) Is this matrix positive definite? (b) What are the corresponding eigenvalues? (c)...

The symmetric matrix

has eigenvectors
x
₁
= (1, −2)
^T

and
x
₂
= (−2, 1)
^T
.

(a) Is this matrix positive definite?

(b) What are the corresponding eigenvalues?

(c) Assuming the starting vector

₀
= (1, −1)
^T

, what eigenvalue will the mower method converge to?

(d) Assuming the calculation in part (c) is finished, explain how to use shifting to compute the other eigenvalue.