Let a E R" be fixed. Suppose that vectors x, y E R" are related by the equation a = x+ (x.y)y. a) Show that ||a|2 – ||x||2 2 + ||y||? = (x.y) b) Deduce that ||a|| > ||x||-
Let a E R" be fixed. Suppose that vectors x, y E R" are related by the equation a = x+ (x.y)y. a) Show that ||a|2 – ||x||2 2 + ||y||? = (x.y) b) Deduce that ||a|| > ||x||-
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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both a and b
Transcribed Image Text:Let a E R" be fixed. Suppose that vectors X, y E R“ are related by the equation
a =x+ (x ·y)y.
a) Show that
||a|° – ||x||?
2 + ||y||?
2.
=(x-y)²
b) Deduce that ||a| ||x||.
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