Determine Whether {V₁, V₂, V₃} Is a Basis for R³

Multiple Choice

Determine whether {v₁, v₂, v₃} is a basis for R³
-Let $\mathrm { H } = \left\{ \left[ \begin{array} { c } \mathrm { a } + 3 \mathrm {~b} + 4 \mathrm {~d} \\ \mathrm { c } + \mathrm { d } \\ - 3 \mathrm { a } - 9 \mathrm {~b} + 4 \mathrm { c } - 8 \mathrm {~d} \\ - \mathrm { c } - \mathrm { d } \end{array} \right] : a , b , c , \mathrm {~d} \right.$ in $\left. \mathscr { R } \right\}$
Find the dimension of the subspace $\mathrm { H }$ .

A) $\operatorname { dim } \mathrm { H } = 2$
B) $\operatorname { dim } \mathrm { H } = 4$
C) $\operatorname { dim } \mathrm { H } = 3$
D) $\operatorname { dim } \mathrm { H } = 1$