Test the linear independence of a) v1=<1,3,5> v2=<2,1,6> v3=<3,4,11> b) u1=<2,1,6> u2=<3,1,7> u3=<5,2,3> Express v3/u3 as linear combination of v1,v2 / u1,u2 when they are linearly dependent otherwise express x=<1,1,1> as linear combination of the given vectors,

Test the linear independence of a) v1=<1,3,5> v2=<2,1,6> v3=<3,4,11> b) u1=<2,1,6> u2=<3,1,7> u3=<5,2,3> Express v3/u3 as linear combination of v1,v2 / u1,u2 when they are linearly dependent otherwise express x=<1,1,1> as linear combination of the given vectors,

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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Test the linear independence of

a) v1=<1,3,5>
v2=<2,1,6>
v3=<3,4,11>

b) u1=<2,1,6>
u2=<3,1,7>
u3=<5,2,3>

Express v3/u3 as linear combination of v1,v2 / u1,u2 when they are linearly dependent
otherwise express x=<1,1,1> as linear combination of the given vectors,

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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Test the linear independence of a) v1=<1,3,5>v2=<2,1,6>v3=<3,4,11> b) u1=<2,1,6>u2=<3,1,7>u3=<5,2,3>Express v3/u3 as linear combination of v1,v2 / u1,u2 when they are linearly dependentotherwise express x=<1,1,1> as linear combination of the given vectors,
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