Kunze Linear Algebra · Problem 3.5.8

Linear Transformations

Mathematics — Methods · basis-for-annihilator

Problem

Let

W

be the subspace of

R^5

which is spanned by the vectors

\alpha_1 = \epsilon_1 + 2\epsilon_2 + \epsilon_3, \quad \alpha_2 = \epsilon_2 + 3\epsilon_3 + 3\epsilon_4 + \epsilon_5,

\alpha_3 = \epsilon_1 + 4\epsilon_2 + 6\epsilon_3 + 4\epsilon_4 + \epsilon_5.

Find a basis for

W^0