|All vectors are in R".Check the true statements below:A. The orthogonal projection of y onto v is the same as the orthogonal projection of y onto cu whenever c + 0.B. An orthogonal matrix is invertible.C. If a set S = {uj,..., up} has the property that u; · u; = 0 whenever i + j, then S is an orthonormal set.|D. If the columns of an m x n matrix A are orthonormal, then the linear mapping a → Ar preserves lengths.E. Not every orthogonal set in R" is a linearly independent set.

Orthogonal Matrix: A is said to be orthogonal matrix AAT=ATA=I, where AT is transpose of A and I is…

DA. The orthogonal projection of y onto v is the same as the orthogonal projection of y onto cu whenever c + 0. B. An orthogonal matrix is invertible. |C. If a set S = {u1,.., up} has the property that u; - uj = 0 whenever i j, then S is an orthonormal set. D. If the columns of an m x n matrix A are orthonormal, then the linear mapping r → Ar preserves lengths. DE. Not every orthogonal set in R" is a linearly independent set.

DA. The orthogonal projection of y onto v is the same as the orthogonal projection of y onto cu whenever c + 0. B. An orthogonal matrix is invertible. |C. If a set S = {u1,.., up} has the property that u; - uj = 0 whenever i j, then S is an orthonormal set. D. If the columns of an m x n matrix A are orthonormal, then the linear mapping r → Ar preserves lengths. DE. Not every orthogonal set in R" is a linearly independent set.

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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Question

|All vectors are in R".
Check the true statements below:
A. The orthogonal projection of y onto v is the same as the orthogonal projection of y onto cu whenever c + 0.
B. An orthogonal matrix is invertible.
C. If a set S = {uj,..., up} has the property that u; · u; = 0 whenever i + j, then S is an orthonormal set.
|D. If the columns of an m x n matrix A are orthonormal, then the linear mapping a → Ar preserves lengths.
E. Not every orthogonal set in R" is a linearly independent set.

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