Question: Suppose that 4 vectors, v1, v2, v3, and v4 are given in $R_{6}$ and we don’t know whether or not these vectors are linearly independent. Explain how you would find the (projection) matrix which projects onto the subspace S = span {v1, v2, v3, v4}.

Is it correct to say: First find the basis of S to obtain a linearly independent columns of a matrix A that will span S. Then use the basis vectors as the columns of A. To find the projection matrix we use $P=A(A^{T}A)^{-1}A^{T}$.

Thats all I got in explaining the process. Is this correct?