Let V be an inner product space. Which of the following is not correct?O A. None in the given list.© B. ||u + w||² + ||u − w|| ²2 =2||||²+2||w||²2 for any u, w€ V.OC.u+w|≤||||+||w|| for any u, w € V.OD. Ku.w|≤|uw|forall u, w€ V.OE. ||u+w|²|u||²+ ||w||² for all u,w EV.

Let V be an inner product space. Which of the following is not correct? O A. None in the given list. ○ B. ||u + w||²³ + ||u − w|22||||²+2||w|2 for any u, w€ V. Ocu+w|≤|u|+||w| for any u, w€ V. OD. Ku.w|≤|uw|| for all u, w€ V. OE.u+w|²||||²+ ||w|² for all u,w EV.

Let V be an inner product space. Which of the following is not correct? O A. None in the given list. ○ B. ||u + w||²³ + ||u − w|22||||²+2||w|2 for any u, w€ V. Ocu+w|≤|u|+||w| for any u, w€ V. OD. Ku.w|≤|uw|| for all u, w€ V. OE.u+w|²||||²+ ||w|² for all u,w EV.

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

Let V be an inner product space. Which of the following is not correct?
O A. None in the given list.
© B. ||u + w||² + ||u − w|| ²2 =2||||²+2||w||²2 for any u, w€ V.
OC.u+w|≤||||+||w|| for any u, w € V.
OD. Ku.w|≤|uw|for
all u, w€ V.
OE. ||u+w|²|u||²+ ||w||² for all u,w EV.

Expert Solution

Step 1

We know the definition of inner product space,

A vector space together with an inner product on it is called inner product space.

For $u, v, w$ vectors and $α$ be scalar then inner product space satisfies following properties.

$<u + v, w> = <u, w> + <v, w>$

$<α v, w> = α <v, w>$

$<v, w> = <w, v>$

$<v, v> \geq 0$ and equal if and only if $v = 0 .$

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