Consider the following linear system of equations a₁₁x₁ + a₁2x₂=b₁ a2₁x₁ + a22x₂=b₂ to carry out and demonstrate Gauss Elimintion procedure, elimination of a21 from the second equation by using superposition and linear principles of linear equations is done by multiplying the second equation by a₁1 and the first by -a21. Show that the result is then -a2₁²₁1x₁-a₂₁@₁2X₂ = -a₂₁b₁ a₁₁₂₁x₁+a₁₁@₂x₂= a₁b²₂ (a) Continue this calculation following the procedure demonstrated in lecture notes Chapter 3, and find the expessions for x₂ and x₁ successively in terms of the constants indicated by the members (terms) in matrix A:
Consider the following linear system of equations a₁₁x₁ + a₁2x₂=b₁ a2₁x₁ + a22x₂=b₂ to carry out and demonstrate Gauss Elimintion procedure, elimination of a21 from the second equation by using superposition and linear principles of linear equations is done by multiplying the second equation by a₁1 and the first by -a21. Show that the result is then -a2₁²₁1x₁-a₂₁@₁2X₂ = -a₂₁b₁ a₁₁₂₁x₁+a₁₁@₂x₂= a₁b²₂ (a) Continue this calculation following the procedure demonstrated in lecture notes Chapter 3, and find the expessions for x₂ and x₁ successively in terms of the constants indicated by the members (terms) in matrix A:
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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![Consider the following linear system of equations
a₁₁x₁ + a₁2x₂=b₁₂
a₂₁x₁ + a22x₂=b₁₂
to carry out and demonstrate Gauss Elimintion procedure, elimination of a21 from the
second equation by using superposition and linear principles of linear equations is
done by multiplying the second equation by a₁1 and the first by -a21.
Show that the result is then
-a2₁²₁1x₁-a2₁@₁2x₂=-a₂₁b₁
a₁₁₂₁x₁+a₁₁@₂x₂ = a₁₁b²₂
(a) Continue this calculation following the procedure demonstrated in lecture notes
Chapter 3, and find the expessions for x2 and x₁ successively in terms of
the constants indicated by the members (terms) in matrix A:
a₁a12
azi an
Following the procedure elaborated in the Lecture Note Chapter 3 page 66
and following ones.
(b) If the first and second row of the system of linear equations
[4] =
a₁a12
a21 a X₂
are interchanged, the equation becomes
a21x₁ + a₂2x₂=b₂
a₁₁x₁+a₁2x₂=b₁
Continue following previous procedure, and demonstrate/ verify that you will
arrive at the expression
ax₂ +
222
x₂ =b₂
(-a₁₁a22+ a₂₁₁₂2) x₂ = a₁b₂+ a₂₁b₁
find the expessions for x₂ and x₁ successively in terms of the constants
indicated by the members (terms) of matrix A
[4]-[4]-[22]
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f1b6c9e-2fed-4e74-93fe-39c8623bed2a%2F2bf39fdd-083a-4738-aeea-d50dd53829c7%2F91fgq3o.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following linear system of equations
a₁₁x₁ + a₁2x₂=b₁₂
a₂₁x₁ + a22x₂=b₁₂
to carry out and demonstrate Gauss Elimintion procedure, elimination of a21 from the
second equation by using superposition and linear principles of linear equations is
done by multiplying the second equation by a₁1 and the first by -a21.
Show that the result is then
-a2₁²₁1x₁-a2₁@₁2x₂=-a₂₁b₁
a₁₁₂₁x₁+a₁₁@₂x₂ = a₁₁b²₂
(a) Continue this calculation following the procedure demonstrated in lecture notes
Chapter 3, and find the expessions for x2 and x₁ successively in terms of
the constants indicated by the members (terms) in matrix A:
a₁a12
azi an
Following the procedure elaborated in the Lecture Note Chapter 3 page 66
and following ones.
(b) If the first and second row of the system of linear equations
[4] =
a₁a12
a21 a X₂
are interchanged, the equation becomes
a21x₁ + a₂2x₂=b₂
a₁₁x₁+a₁2x₂=b₁
Continue following previous procedure, and demonstrate/ verify that you will
arrive at the expression
ax₂ +
222
x₂ =b₂
(-a₁₁a22+ a₂₁₁₂2) x₂ = a₁b₂+ a₂₁b₁
find the expessions for x₂ and x₁ successively in terms of the constants
indicated by the members (terms) of matrix A
[4]-[4]-[22]
=
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