Determine whether the statement below is true or false. Justify the answer. Assume all vectors and subspaces are in Rn.The orthogonal projection y (see pic) of y onto a subspace W can sometimes depend on the orthogonal basis for W used to compute y(see pic). Determine whether the statement below is true or false. Justify the answer. Assume all vectors and subspaces are in R".The orthogonal projection y of y onto a subspace W can sometimes depend on the orthogonal basis for W used to compute y.Choose the correct answer below.O A. The statement is false. The uniqueness property of the orthogonal decomposition y = y +z indicates that, no matter the basis used to find it, thedecomposition will always be the same.OB.The statement is true. For each possible orthogonal basis of W, y is expressed as a different linear combination of the vectors in that basis.O C. The statement is true. The orthogonal projection y of y onto a subspace W depends on an orthonormal basis for W.O D. The statement is false. The orthogonal projection y of y onto a subspace W depends on an orthonormal basis for W.

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Answered: Determine whether the statement below…

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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Determine whether the statement below is true or false. Justify the answer. Assume all vectors and subspaces are in Rⁿ.
The orthogonal projection y (see pic) of y onto a subspace W can sometimes depend on the orthogonal basis for W used to compute y(see pic).

Determine whether the statement below is true or false. Justify the answer. Assume all vectors and subspaces are in R".
The orthogonal projection y of y onto a subspace W can sometimes depend on the orthogonal basis for W used to compute y.
Choose the correct answer below.
O A. The statement is false. The uniqueness property of the orthogonal decomposition y = y +z indicates that, no matter the basis used to find it, the
decomposition will always be the same.
OB.
The statement is true. For each possible orthogonal basis of W, y is expressed as a different linear combination of the vectors in that basis.
O C. The statement is true. The orthogonal projection y of y onto a subspace W depends on an orthonormal basis for W.
O D. The statement is false. The orthogonal projection y of y onto a subspace W depends on an orthonormal basis for W.

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