Kunze Linear Algebra · Problem 2.6.3

Vector Spaces

Mathematics — Methods · subspace-as-solution-space

Problem

Consider the vectors in

R^4

defined by

\alpha_1 = (-1, 0, 1, 2), \quad \alpha_2 = (3, 4, -2, 5), \quad \alpha_3 = (1, 4, 0, 9).

Find a system of homogeneous linear equations for which the space of solutions is exactly the subspace of

R^4

spanned by the three given vectors.