Linear algebra: please solve q41 and 43 correctly and handwritten. Values are also attached In Exercises 40-45, express the given vector b as a lin-ear combination of v₁ and v2, where v₁ and v₂ are inEq. (10).40. b =2[²]70-[:]442. b =[3]41. b =43. b =0[:] The vectors listed in Eq. (10) are used in several of theexercises that follow.2--8--8--8-[3].V2V12--)--[]V50336------0-0-0U422=42[3](10)

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Answered: In Exercises 40-45, express the given…

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: please solve q41 and 43 correctly and handwritten. Values are also attached

In Exercises 40-45, express the given vector b as a lin-
ear combination of v₁ and v2, where v₁ and v₂ are in
Eq. (10).
40. b =
2
[²]
7
0
-[:]
4
42. b =
[3]
41. b =
43. b =
0
[:]

The vectors listed in Eq. (10) are used in several of the
exercises that follow.
2
--8--8--8
-[3].
V2
V1
2
--)--[]
V5
0
3
3
6
----
--0-0-0
U4
2
2
=
4
2
[3]
(10)

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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