All vectors and subspaces arc in Rm Check the true statement

All vectors and subspaces arc in R^m. Check the true statements below: Assume A is an m X n matrix with n linearly independent columns. In a QR factorization A = QR of A the columns of Q form an orthonormal basis for the column space of A. If the vector v is not in the subspace W of R^m, then v - proj_w, (v) denotes the projection of v onto the subspace W and o denotes the zero vector in R^m. If W = span{w_1, W_2, W_3} where {W_1, W_2, W_3} is a linearly independent set, and if {u_1, u_2} is an orthogonal set in W, then {u_1, u_2} is an orthogonal basis for W.

Solution

A. TRUE

B. TRUE

C. TRUE, The Gram-Schmidt process produces from a linearly independent set {x1, . . . , xp} and orthogonal set {v₁, . . . , v_p} with the property that for each k, the vectors v₁, . . . v_k span the same subspace as the spanned by x₁, . . . x_k .