*2. Decide whether each of the following sets of vectors is linearly independent. a. {(1, 4), (2, 9)}C R² b. {(1,4, 0), (2, 9, 0)} C R³ c. {(1, 4, 0), (2, 9, 0), (3, –2, 0)} CR³ d. {(1, 1, 1), (2, 3, 3), (0, 1, 2)} C R³

*2. Decide whether each of the following sets of vectors is linearly independent. a. {(1, 4), (2, 9)}C R² b. {(1,4, 0), (2, 9, 0)} C R³ c. {(1, 4, 0), (2, 9, 0), (3, –2, 0)} CR³ d. {(1, 1, 1), (2, 3, 3), (0, 1, 2)} C R³

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.CR: Review Exercises

Problem 78CR: Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set...

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Question

linear algebra 3.3 Q2 sub question a, c, d

3 Linear Independence and Basis
155
*2. Decide whether each of the following sets of vectors is linearly independent.
а. ((1,4), (2, 9)} C R
b. {(1,4, 0), (2, 9, 0)} С R3
с. {(1,4, 0), (2, 9,0), (3, —2, 0)} CR3
d. {(1, 1, 1), (2, 3, 3), (0, 1, 2)} C R³
е. {(1, 1, 1, 3), (1, 1, 3, 1), (1, 3, 1, 1), (3, 1, 1, 1)} R*
f. {(1, 1, 1, –3), (1, 1, – 3, 1), (1, –3, 1, 1), (-3, 1, 1, 1)} C R*

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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