For each of the vector spaces below with specified bases B, find the coordinate vector [v]B of the given vector v with respect to B. (a) V = R3, B = {(1, 0, 3),(2, 1, 8),(1, −1, 2)}, v = (3, −5, 4). (b) V = P2(R), B = {1 + t2, t + t2, 1 + 2t + t2}, v = 1 + 4t + 7t2.

For each of the vector spaces below with specified bases B, find the coordinate vector [v]B of the given vector v with respect to B. (a) V = R3, B = {(1, 0, 3),(2, 1, 8),(1, −1, 2)}, v = (3, −5, 4). (b) V = P2(R), B = {1 + t2, t + t2, 1 + 2t + t2}, v = 1 + 4t + 7t2.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 12CM

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Question

For each of the vector spaces below with specified bases B, find the coordinate vector [v]_B of the given vector v with respect to B. (a) V = R³, B = {(1, 0, 3),(2, 1, 8),(1, −1, 2)}, v = (3, −5, 4). (b) V = P₂(R), B = {1 + t², t + t², 1 + 2t + t²}, v = 1 + 4t + 7t².

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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