Solving Ax=b in Parametric Vector Form | System A = 0...-2...9...5, b = 0...0

Click For Summary
SUMMARY

The discussion focuses on solving the linear system Ax=b, where matrix A is defined as [[0, -2, 9, 5], [0, 1, 2, -6]] and vector b is [0, 0]. The user has derived an intermediate matrix [[1, 0, 13, 7, 0], [0, 1, 2, -6, 0]] and is seeking guidance on converting this into parametric vector form. The presence of two leading ones indicates the existence of free variables, which is crucial for expressing the solution in parametric form.

PREREQUISITES
  • Understanding of linear algebra concepts, specifically systems of linear equations.
  • Familiarity with matrix operations and row reduction techniques.
  • Knowledge of parametric vector representation of solutions.
  • Ability to identify leading and free variables in a matrix.
NEXT STEPS
  • Study the method of Gaussian elimination for solving systems of equations.
  • Learn about the concept of free variables in linear algebra.
  • Research how to express solutions in parametric vector form.
  • Explore examples of similar linear systems to reinforce understanding.
USEFUL FOR

Students and educators in linear algebra, particularly those focusing on solving systems of equations and understanding parametric vector forms.

Precursor
Messages
219
Reaction score
0
Homework Statement

Describe the solution(s) of the system Ax=b in parametric vector form where A =
[tex]0...-2...9...5[/tex]
[tex]0...1...2...-6[/tex]

and b =
[tex]0[/tex]
[tex]0[/tex]

The attempt at a solution
I got this far:

[tex]1...0...13...7...0[/tex]
[tex]0...1...2...-6...0[/tex]

How do I continue to get it into parametric vector form? I only have two leading ones, so does it look like I'll be getting some free variables?
 
Last edited:
Physics news on Phys.org
Any suggestions?
 
Is my work confusing?
 

Similar threads

Evaluate the given integrals - line integrals
  • · Replies 2 ·
Replies
2
Views
1K
MHB -311.1.5.8 Ax=b in parametric vector form,
  • · Replies 7 ·
Replies
7
Views
1K
Linear independence of Coordinate vectors as columns & rows
  • · Replies 2 ·
Replies
2
Views
2K
MHB 311.1.5.12 Ax=0 in parametric vector form
  • · Replies 7 ·
Replies
7
Views
2K
Parametric Equation of a line, Conditions
  • · Replies 3 ·
Replies
3
Views
4K
Parametric equation and vector equation
  • · Replies 10 ·
Replies
10
Views
2K
Solving ##y'' - 5 y' - 6y = e^{3x}## using Laplace Transform
  • · Replies 7 ·
Replies
7
Views
2K
Which statements are true given a solution to the system x'=Ax?
  • · Replies 6 ·
Replies
6
Views
2K
Find the equation of the curve given: ##\frac{dy}{dx}=2(kx-1)^5##
  • · Replies 3 ·
Replies
3
Views
2K
Show: Vectors e.g.(a,b,1) do not form vector space.
  • · Replies 2 ·
Replies
2
Views
3K