All vectors and subspaces are in R". Note you only have 5 attempts for this question. Check the true statements below: A. If z is orthogonal to ₁ and 2 and if W=span(1, 2), then z must be in W. B. For each and each subspace W, the vector - projw(y) is orthogonal to W. C. If y is in a subspace W, then the orthogonal projection of y onto W is y itself. D. If a matrix A is such that AT = A then the perpendicular complement of the kernel of A is the image of A. E. The orthogonal projection of y onto a subspace W can sometimes depend on the matrix used to compute z. F. If y = Z1 + Z2, where Z₁ is in a subspace W and 22 is in W-, then 2₁ must be the orthogonal projection of ij onto W. G. The closest vector to y in a subspace W is given by the vector - projw(y). H. The columns of a matrix A are perpendicular to the rows of AT I. If W is a subspace and if is in both W and W, then must be the zero vector.

All vectors and subspaces are in R". Note you only have 5 attempts for this question. Check the true statements below: A. If z is orthogonal to ₁ and 2 and if W=span(1, 2), then z must be in W. B. For each and each subspace W, the vector - projw(y) is orthogonal to W. C. If y is in a subspace W, then the orthogonal projection of y onto W is y itself. D. If a matrix A is such that AT = A then the perpendicular complement of the kernel of A is the image of A. E. The orthogonal projection of y onto a subspace W can sometimes depend on the matrix used to compute z. F. If y = Z1 + Z2, where Z₁ is in a subspace W and 22 is in W-, then 2₁ must be the orthogonal projection of ij onto W. G. The closest vector to y in a subspace W is given by the vector - projw(y). H. The columns of a matrix A are perpendicular to the rows of AT I. If W is a subspace and if is in both W and W, then must be the zero vector.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 48E

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