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All vectors and subspaces are in R™. Check the true statements below: A. If the vector v is not in the subspace W of R", then v - projw (v) is not 0, where projw (v) denotes the projection of v onto the subspace W and 0 denotes the zero vector in R™. B. If W = span{w₁, W2, W3} where {w₁, W2, W3} is a linearly independent set, and if {u₁, u₂} is an orthogonal set in W, then {u₁, u₂} is an orthogonal basis for W. C. Assume A is an m X n matrix with n linearly independent columns. In a QR factorization A = QR of Athe columns of Q form an orthonormal basis for the column space of A.

All vectors and subspaces are in R™. Check the true statements below: A. If the vector v is not in the subspace W of R", then v - projw (v) is not 0, where projw (v) denotes the projection of v onto the subspace W and 0 denotes the zero vector in R™. B. If W = span{w₁, W2, W3} where {w₁, W2, W3} is a linearly independent set, and if {u₁, u₂} is an orthogonal set in W, then {u₁, u₂} is an orthogonal basis for W. C. Assume A is an m X n matrix with n linearly independent columns. In a QR factorization A = QR of Athe columns of Q form an orthonormal basis for the column space of A.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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All vectors and subspaces are in Rm. Check the true statements below: - A. If the vector v is not in the subspace W of Rm, then v – projw (v) is not 0, where projw (v) denotes the projection of v onto the subspace W and 0 denotes the zero vector in R™. B. If W = span{W₁, W2, W3} where {W₁, W2, W3} is a linearly independent set, and if {u₁, u₂} is an orthogonal set in W, then {u₁, u₂} is an orthogonal basis for W. C. Assume A is an m × ʼn matrix with n linearly independent columns. In a QR factorization A = QR of Athe columns of Q form an orthonormal basis for the column space of A.
Transcribed Image Text:All vectors and subspaces are in Rm. Check the true statements below: - A. If the vector v is not in the subspace W of Rm, then v – projw (v) is not 0, where projw (v) denotes the projection of v onto the subspace W and 0 denotes the zero vector in R™. B. If W = span{W₁, W2, W3} where {W₁, W2, W3} is a linearly independent set, and if {u₁, u₂} is an orthogonal set in W, then {u₁, u₂} is an orthogonal basis for W. C. Assume A is an m × ʼn matrix with n linearly independent columns. In a QR factorization A = QR of Athe columns of Q form an orthonormal basis for the column space of A.
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