16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 2.4.1

Vector Spaces

Mathematics — Linear Algebra · ordered-basis-and-coordinates

Problem

Show that the vectors

\alpha_1 = (1, 1, 0, 0), \quad \alpha_2 = (0, 0, 1, 1)

\alpha_3 = (1, 0, 0, 4), \quad \alpha_4 = (0, 0, 0, 2)

form a basis for

R^4

. Find the coordinates of each of the standard basis vectors in the ordered basis

\{\alpha_1, \alpha_2, \alpha_3, \alpha_4\}