The symmetric matrix                                 has eigenvectors x 1 = (1, 1, 0) T , x 2 = (1, 0, 2) T , and x 3 = (0, −2, 1) T . (a) Is this matrix positive definite? (b) What are the...

The symmetric matrix

has eigenvectors
x
₁
= (1, 1, 0)
^T

,
x
₂
= (1, 0, 2)
^T

, and
x
₃
= (0, −2, 1)
^T

.

(a) Is this matrix positive definite?

(b) What are the corresponding eigenvalues?

(c) Assuming the starting vector

₀
= (1, 1, 1)
^T

, what eigenvalue will the power method converge to and what will be the resulting eigenvector?