If , show that if the columns of A are linearly independent, then R must be invertible.
(Hint: Study the equation , and use the fact that .
Need some guidance here.
I tried something like:
And the columns of Q are orthonormal.
So the matrix will have columns formed from the columns of , using the weights in columns of A as weights.
Is it correct to say that even the columns of will be linearly independent?
If so, will have linearly independent columns, and since R is n x n , R is invertible by the Invertible matrix theorem.