Suppose S={r,u,d} is a set of linearly independent vectors. If x=3r+5u+3d, determine whether T={r,u,x} is a linearly independent set. 1. Is T linearly independent or dependent? If T is dependent, enter a non-trivial linear relation below. Otherwise, enter 0's for the coefficients.

Suppose S={r,u,d} is a set of linearly independent vectors. If x=3r+5u+3d, determine whether T={r,u,x} is a linearly independent set. 1. Is T linearly independent or dependent? If T is dependent, enter a non-trivial linear relation below. Otherwise, enter 0's for the coefficients.

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Equations, Inequalities, And Mathematical Modeling

Section1.3: Modeling With Linear Equations

Problem 61E

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Suppose S={r,u,d} is a set of linearly independent vectors.

If x=3r+5u+3d, determine whether T={r,u,x} is a linearly independent set.

1. Is T linearly independent or dependent?

If T is dependent, enter a non-trivial linear relation below. Otherwise, enter 0's for the coefficients.

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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