Let $$A = \left[\begin{array}{ccc} -14 &14 &-7\cr 21 &-19 &10\cr -10 &10 &-5 \end{array}\right],$$ let $\vec{a}_1, \vec{a}_2$ and $\vec{a}_3$ be the columns of $A$, let $\mathcal{B} = \lbrace \vec{a}_1, \vec{a}_2, \vec{a}_3 \rbrace$ and let $H = \mathrm{span}(\mathcal{B})$.

1. The number of vectors in $\mathcal{B}$ is .
   
   
2. The number of vectors in $H$ is .
   
   
3. The dimension of the subspace $H$ is .
   
   
4. Is $\mathcal{B}$ a basis for $\mathbb{R}^{3}$? choose basis for R^3 not a basis for R^3
   
   
5. A basis for the subspace $H$ is $\big\lbrace$ $\big\rbrace$. vector