Consider the following two systems. (a) S-4x - x + 3y Solution to system (a): x = Solution to system (b): x = { y = y = - 4x - 2y A-¹ = || || = 1 (i) Find the inverse of the (common) coefficient matrix of the two systems. (88) -3 2y 3 x + 3y = 2 (ii) Find the solutions to the two systems by using the inverse, i.e. by evaluating A-¹B where B represents the right [3] hand side (i.e. B = for system (a) and B = for system (b)).
Consider the following two systems. (a) S-4x - x + 3y Solution to system (a): x = Solution to system (b): x = { y = y = - 4x - 2y A-¹ = || || = 1 (i) Find the inverse of the (common) coefficient matrix of the two systems. (88) -3 2y 3 x + 3y = 2 (ii) Find the solutions to the two systems by using the inverse, i.e. by evaluating A-¹B where B represents the right [3] hand side (i.e. B = for system (a) and B = for system (b)).
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
![Consider the following two systems.
(a)
(b)
hand side (i.e. B =
A
Solution to system (b): x
=
- 4x - 2y
x + 3y
J-4x - 2y
1 x + 3y
for system (a) and B :
=
y
y =
(i) Find the inverse of the (common) coefficient matrix of the two systems.
[88]
=
=
=
(ii) Find the solutions to the two systems by using the inverse, i.e. by evaluating A-¹B where B represents the right
3
[13]
for system (b)).
2
Solution to system (a): x =
1
-3
=
3
= 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf45d460-f071-413c-8212-21e16655adc4%2F25981a20-b7c4-467b-93fd-a5c5935c2d52%2Fj9glnat_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following two systems.
(a)
(b)
hand side (i.e. B =
A
Solution to system (b): x
=
- 4x - 2y
x + 3y
J-4x - 2y
1 x + 3y
for system (a) and B :
=
y
y =
(i) Find the inverse of the (common) coefficient matrix of the two systems.
[88]
=
=
=
(ii) Find the solutions to the two systems by using the inverse, i.e. by evaluating A-¹B where B represents the right
3
[13]
for system (b)).
2
Solution to system (a): x =
1
-3
=
3
= 2
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