All vectors and subspaces are in ${\mathbb R}^n$.

Check the true statements below:

A. If $A=QR$, where $Q$ has orthonormal columns, then $R=Q^{T}A$.
B. If $\{ v_{1},v_{2},v_{3} \}$ is an orthogonal basis for $W$, then multiplying $v_{3}$ by a scalar $c$ gives a new orthogonal basis $\{ v_{1},v_{2},cv_{3} \}$.
C. The Gram-Schmidt process produces from a linearly independent set $\{ x_{1},...,x_{p} \}$ an orthogonal set $\{ v_{1},...,v_{p} \}$ with the property that for each $k$, the vectors $v_{1},...,v_{k}$ span the same subspace as that spanned by $x_{1},...,x_{k}$.