A First Course in Linear Algebra · Problem B.C11

Vector Spaces — Robert Beezer

Mathematics — Linear Algebra · basis-subspace

Problem

Find a basis for the subspace

W

\mathbb{C}^4

W = \left\{\begin{bmatrix}a+b-2c\\a+b-2c+d\\-2a+2b+4c-d\\b+d\end{bmatrix}\,\middle|\, a,b,c,d \in \mathbb{C}\right\}