a) Let S = {v1, v2, V3}be a linearly independent set of vectors in R³. Determinewhether T = {2v1 +v2 – 2v3,4v1 + 3v2 , 3v1 + 2v2independent.v3} is linearlyb) Describe all vectors b that can be written as linear combinations of the[4]vectors v, =,V2 =,V3 =|2

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a) Let S = {v1, v2, V3} be a linearly independent set of vectors in R³. Determine whether T = {2v1 +v2 – 2v3,4v1 + 3v2 , 3v1 + 2v2 – v3} _is linearly independent. b) Describe all vectors b that can be written as linear combinations of the 4 vectors vị = = [2|,v3 =|2 |2] |3

a) Let S = {v1, v2, V3} be a linearly independent set of vectors in R³. Determine whether T = {2v1 +v2 – 2v3,4v1 + 3v2 , 3v1 + 2v2 – v3} _is linearly independent. b) Describe all vectors b that can be written as linear combinations of the 4 vectors vị = = [2|,v3 =|2 |2] |3

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

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

a) Let S = {v1, v2, V3}be a linearly independent set of vectors in R³. Determine
whether T = {2v1 +v2 – 2v3,4v1 + 3v2 , 3v1 + 2v2
independent.
v3} is linearly
b) Describe all vectors b that can be written as linear combinations of the
[4]
vectors v, =
,V2 =
,V3 =
|2

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