Linear algebra: c=4 please asap (a) Show that the vectors v₁ = (1,-1,2), v₂ = (2,-1, 3) and v3 = (3,c + 1,2 c) do not spanR³ and describe geometrically span{v1, U2, U3}. Does the set {v1, U2, U3} construct a basis forR³ ? Explain.(b) Find the Wronskian of the functions fi(x) = (c+ 1)ea and f2(x) = ex where a, b € R.Determine the condition(s) on a, b such that these functions are linearly independent on anyinterval.

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Answered: (a) Show that the vectors v₁ =…

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: c=4 please asap

(a) Show that the vectors v₁ = (1,-1,2), v₂ = (2,-1, 3) and v3 = (3,c + 1,2 c) do not span
R³ and describe geometrically span{v1, U2, U3}. Does the set {v1, U2, U3} construct a basis for
R³ ? Explain.
(b) Find the Wronskian of the functions fi(x) = (c+ 1)ea and f2(x) = ex where a, b € R.
Determine the condition(s) on a, b such that these functions are linearly independent on any
interval.

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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