Answered: Linear algebra question - determine if…

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 question - determine if set of vectors is linearly independent or linearly dependent - if linearly dependent, express one of the vectors in the set as a linear combination fo the others.

I have attached my work but getting marked incorrect for some reason, not sure why. Clearly marked steps would be helpful to better understand.

Thank you.

Lineau
combination:
=
------
=
1
5
3.
X₁v₁ + X₂ √₂ + x3 √3 = 0 → non-trivial solution →
X1-4X3=0
=
x₂ + 3x3 = 07
11
6.
→ x₁ = 4X3
X₂=-3X₂
231
viet
뼈를
-110
110
-60
5
3 2
RREF=
O O
00
=) X3 is arbitrary + if X₂ =
O
O
0
linearly dependent)
then
X₁=4/1)=4
x₂ = 3(1)=-

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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