A First Course in Linear Algebra · Problem S-RQ2

Vector Spaces — Robert Beezer

Mathematics — Linear Algebra · subspace-testing

Problem

Consider the set of vectors

W = \left\{ \begin{bmatrix} a \\ b \\ c \end{bmatrix} \,\middle|\, 3a - 2b + c = 5 \right\}

Is the set

W

a subspace of

\mathbb{C}^3

? Explain your answer.