Answered: x₁2x₂+x3 + x4 = 4 x₁ + 2x₂ + x3 + x4 =…

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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Question

Linear algebra question: use Gauss-Jordan Elimination techniques to solve system of equation. If system is consistent, write answer in terms of free variables.

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.

x₁2x₂ + x3 + x4 = 4
x₁ + 2x₂ + x3 + x4 = 1
2x1
+2x3 + 2x4 = 5

Free
RREF= X₁ X₂
(
O
I
variables:
x
+
X3
Ху
O
X₂ = 0
JJ
=
O
+ X₂
4
X₂ X4
1
1
O
1)
f Xu
x4
x₁ =
-X₁ - Xy
2/2 - x₁ - x₂₂
0
GIN
들
도
O
52-X3 X4
consistent

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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