Which is(are) true?? a. If W=span{w1,w2,w3} where {w1,w2,w3} is a linearly indep

Question

Which is(are) true?? a. If W=span{w1,w2,w3} where {w1,w2,w3} is a linearly independent set, and if {u1,u2} is an orthogonal set in , then {u1,u2} is an orthogonal basis for W. b. Assume A is an m by 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. c. If the vector v is not in the subspace Wof R^m, then v - proj _w (v) is not 0, where proj _w (v) denotes the projection of v onto the subspace W and 0 denotes the zero vector in R^m.

Explanation / Answer

b. Assume A is an m by 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.

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