Problem 5. 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 + ||y||? (x ·y)² (b) Deduce that ||a|| > ||x||.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Problem 5. Let a E R" be fixed. Suppose that vectors x, y E R" are related by the equation
а — х+ (x:у)у.
(a) Show that
||a||² – ||x||²
2 + ||y||²
-
(x - y)?
(b) Deduce that ||a|| > ||x||.
Transcribed Image Text:Problem 5. Let a E R" be fixed. Suppose that vectors x, y E R" are related by the equation а — х+ (x:у)у. (a) Show that ||a||² – ||x||² 2 + ||y||² - (x - y)? (b) Deduce that ||a|| > ||x||.
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