a) Detemine whether this set of vectors is orthogonal? Q. No. 3 -2 8. 4 1 b) Detemine if the following systemis consistent? x2 - 4x3 = 8 2х, — 3х, + 2х, — 1 5x, - 8x2 + 7x3 = 1 c) Let R? have the weighted Euclidean inner product, < u, v > = 2u, v, + 3uzv2, and let u = (1,1),v = (3,2), w = (0,1) andk = 3. Compute the following quantities, (1). < u, v >, (ii). < kv, w >, (iii). < u + v, w >. d) Detemine if b is a linear combination of a,, az and az? [0] ass b = 8
a) Detemine whether this set of vectors is orthogonal? Q. No. 3 -2 8. 4 1 b) Detemine if the following systemis consistent? x2 - 4x3 = 8 2х, — 3х, + 2х, — 1 5x, - 8x2 + 7x3 = 1 c) Let R? have the weighted Euclidean inner product, < u, v > = 2u, v, + 3uzv2, and let u = (1,1),v = (3,2), w = (0,1) andk = 3. Compute the following quantities, (1). < u, v >, (ii). < kv, w >, (iii). < u + v, w >. d) Detemine if b is a linear combination of a,, az and az? [0] ass b = 8
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
![a) Detemine whether this set of vectors is orthogonal?
Q. No. 3
-2
8.
4 1
b) Detemine if the following systemis consistent?
x2 - 4x3 = 8
2х, — 3х, + 2х, — 1
5x, - 8x2 + 7x3 = 1
c) Let R? have the weighted Euclidean inner product,
< u, v > = 2u, v, + 3uzv2,
and let u = (1,1),v = (3,2), w = (0,1) andk = 3.
Compute the following quantities,
(1). < u, v >, (ii). < kv, w >, (iii). < u + v, w >.
d) Detemine if b is a linear combination of a,, az
and az?
[0]
ass
b =
8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc959f986-70aa-402d-958e-dd5e0724164c%2Fe23ca3cd-d006-40f1-a7c5-a9c00275d77b%2Fcohaxx_processed.png&w=3840&q=75)
Transcribed Image Text:a) Detemine whether this set of vectors is orthogonal?
Q. No. 3
-2
8.
4 1
b) Detemine if the following systemis consistent?
x2 - 4x3 = 8
2х, — 3х, + 2х, — 1
5x, - 8x2 + 7x3 = 1
c) Let R? have the weighted Euclidean inner product,
< u, v > = 2u, v, + 3uzv2,
and let u = (1,1),v = (3,2), w = (0,1) andk = 3.
Compute the following quantities,
(1). < u, v >, (ii). < kv, w >, (iii). < u + v, w >.
d) Detemine if b is a linear combination of a,, az
and az?
[0]
ass
b =
8
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