Linear Algebra **Consider the set** \( S = \{ (2,4), (-1,-2), (0,6) \} \).**(a)** Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector.**(b)** Express one of the vectors in the set as a linear combination of the other vectors in the set.

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Linear Algebra

**Consider the set** \( S = \{ (2,4), (-1,-2), (0,6) \} \).

**(a)** Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector.

**(b)** Express one of the vectors in the set as a linear combination of the other vectors in the set.

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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