Determine Whether {V₁, V₂, V₃} Is a Basis for R³ $\left\{ \left[ \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right] , \left[ \begin{array} { l } 0 \\ 1 \\ 2 \end{array} \right] \right\}$

Multiple Choice

Determine whether {v₁, v₂, v₃} is a basis for R³
-Given the set of vectors $\left\{ \left[ \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right] , \left[ \begin{array} { l } 0 \\ 1 \\ 2 \end{array} \right] \right\}$ , decide which of the following statements is true:
A: Set is linearly independent and spans $R ^ { 3 }$ . Set is a basis for $R ^ { 3 }$ .
B: Set is linearly independent but does not span $R ^ { 3 }$ . Set is not a basis for $R ^ { 3 }$ .
C: Set spans $\mathscr { R } ^ { 3 }$ but is not linearly independent. Set is not a basis for $R ^ { 3 }$ .
D: Set is not linearly independent and does not span $R ^ { 3 }$ . Set is not a basis for $R ^ { 3 }$ .

A) B
B) $\mathrm { D }$
C) $\mathrm { C }$
D) $\mathrm { A }$