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
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 30EQ
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