Find a Matrix a Such That W = Col A $\left\{ \mathrm { p } _ { 1 } , \mathrm { p } _ { 2 } , \mathrm { p } _ { 3 } \right\}$

Multiple Choice

Find a matrix A such that W = Col A.
-A: The set $\left\{ \mathrm { p } _ { 1 } , \mathrm { p } _ { 2 } , \mathrm { p } _ { 3 } \right\}$ where $\mathrm { p } _ { 1 } ( \mathrm { t } ) = 1 , \mathrm { p } _ { 2 } ( \mathrm { t } ) = \mathrm { t } ^ { 2 } , \mathrm { p } _ { 3 } ( \mathrm { t } ) = 1 + 5 \mathrm { t }$
B: The set $\left\{ p _ { 1 } , p _ { 2 } , p _ { 3 } \right\}$ where $p _ { 1 } ( t ) = t , p _ { 2 } ( t ) = t ^ { 2 } , p _ { 3 } ( t ) = 2 t + 5 t ^ { 2 }$
$C :$ The set $\left\{ \mathbf { p } _ { 1 } , \mathbf { p } _ { 2 } , \mathbf { p } _ { 3 } \right\}$ where $\mathbf { p } _ { 1 } ( t ) = 1 , \mathbf { p } _ { 2 } ( t ) = t ^ { 2 } , \mathbf { p } _ { 3 } ( t ) = 1 + 5 t + t ^ { 2 }$

A) $A$ and $C$
B) A only
C) all of them
D) B only
E) C only