Find a Basis for the Column Space of the Matrix $\mathrm { P } _ { 7 }$

Multiple Choice

Find a basis for the column space of the matrix.
-Determine which of the following statements is false.
A: The dimension of the vector space $\mathrm { P } _ { 7 }$ of polynomials is 8 .
$B$ : Any line in $R ^ { 3 }$ is a one-dimensional subspace of $R ^ { 3 }$ .
$C :$ If a vector space $\mathrm { V }$ has a basis $B = \left\{ b _ { 1 } , \ldots . . , b _ { 7 } \right\}$ , then any set in $\mathrm { V }$ containing 8 vectors must be linearly dependent.

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