Hi

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:

But

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.

Thanks!