a) Let U be an m xn matrix with orthonormal columns, and x and y be in R". Theni.| Ux l=1 x|(Ux) · (Uy) = x•yiii.(Ux) · (Uy) = 0 if and only if x y = 0.b) Let A =* Explain why A* approaches o-5 -751as k - 00.L4 1.21.50Answer:

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Answered: a) Let U be an m xn matrix with…

a) Let U be an m xn matrix with orthonormal columns, and x and y be in R". Then I Ux I=I x| (Ux) (Uy) = x y i. (Ux) (Uy) = 0 if and only if x y = 0.

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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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

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a) Let U be an m xn matrix with orthonormal columns, and x and y be in R". Then
i.
| Ux l=1 x|
(Ux) · (Uy) = x•y
iii.
(Ux) · (Uy) = 0 if and only if x y = 0.
b) Let A =* Explain why A* approaches o
-5 -751
as k - 00.
L4 1.2
1.50
Answer:

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