Consider the fold 2x₁ - 8x₁ 5x1 2 - 4x3 = 7 +6x3 = -3 + 2x2 -9x3 = 15 14 -6 +3x₂ +4x2 30 2X1 - 8x1 5x1 +3x2 +4x2 + 2x2 - 4x3 It can be shown that the first system has a solution. Use this fact and the theory of null spaces and column spaces of matrices to explain why the seco system must also have a solution. (Make no row operations.) Next, determine the relationship between the first vector of constraints, b = = 14 = -6 +6x3 -9x3 = 30 C... 7 -3, and the second vector of constraints. 15
Consider the fold 2x₁ - 8x₁ 5x1 2 - 4x3 = 7 +6x3 = -3 + 2x2 -9x3 = 15 14 -6 +3x₂ +4x2 30 2X1 - 8x1 5x1 +3x2 +4x2 + 2x2 - 4x3 It can be shown that the first system has a solution. Use this fact and the theory of null spaces and column spaces of matrices to explain why the seco system must also have a solution. (Make no row operations.) Next, determine the relationship between the first vector of constraints, b = = 14 = -6 +6x3 -9x3 = 30 C... 7 -3, and the second vector of constraints. 15
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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Can someone please explain to me ASAP??!!!
Transcribed Image Text:O
с
Consider the following two systems of equations.
= 7
2x1
+3x2
- 4x3
- 8x₁ +4x2 +6x3 = -3
5x₁ +2x₂ -9x3 = 15
b
It can be shown that the first system has a solution. Use this fact and the theory of null spaces and column spaces of matrices to explain why the second
system must also have a solution. (Make no row operations.)
Textbook
Next, determine the relationship between the first vector of constraints, b =
14
-6
2X1
-8x1
30
5x1
Ask my instructor
+3x2
- 4x3 = 14
+4x₂
+6x3
=-6
+ 2x2 - 9x3 = 30
TT
7
-3, and the second vector of constraints.
15
Clear all
Check answer
Transcribed Image Text:Consider the following two systems of equations.
2x1
= 7
+3x₂
- 4x3
-8x₁
+4x2
+ 6x3 = -3
5x₁ +2x₂ -9x3 = 15
space Col A.
2X1
-8x1
5x₁
Textbook Ask my instructor
+3x₂
+4x2
It can be shown that the first system has a solution. Use this fact and the theory of null spaces and column spaces of matrices to explain why the second
system must also have a solution. (Make no row operations.)
Convright ©20
+ 2x2
- 4x3 = 14
+ 6x3 = -6
-9x3 = 30
Let A be the coefficient matrix of the given system of equations. Since the first system has a solution, the constant vector b =
- 3
W
15
Next, determine the relationship between the first vector of constraints, b = -3, and the second vector of constraints.
7
Clear all
is in the vector
Check answer
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