Each vector in the basis set for Rn, needs to be n-components tall

• We showed that for $B$ to be a basis for $R^n$, it needs to have $n$ vectors.
• Now each of those vectors also should have $n$ components–i.e. be $n$ entries tall. Since we want to represent all the components of any vector in $R^n$.
• Constructing $A=[{\vec{v}}_1...{\vec{v}}_n]$ where $B=\{{\vec{v}}_1,...,{\vec{v}}_n\}$. This means that each of the rows in the matrix $A$ must have a non-zero entry and hence have a pivot.
• I.e. the matrix $A$ must have rank $n$.