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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 16E
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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
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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