please help me on this quesion All vectors and subspaces are

please help me on this quesion

All vectors and subspaces are in R^n. Check the true statements below: If A = QR. where Q has orthonormal columns, then R = Q^T A. 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}. 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.

Solution

# (a) : Given :

A = QR

where Q has orthoonrmal columns

then R = Q^TA is TRUE .