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

In summary, Parametric Vector Form is a mathematical representation of a vector in terms of parameters. It is commonly used in vector calculus and physics to describe the motion of objects in space. It differs from Cartesian Vector Form in that it uses parameters rather than components to represent vectors. This allows for a more general representation and makes it easier to manipulate and solve problems involving vectors. In physics, Parametric Vector Form is used to describe the motion of objects, and it can be used in any number of dimensions.
  • #1
Precursor
222
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
  • #2
Any suggestions?
 
  • #3
Is my work confusing?
 

1. What is Parametric Vector Form?

Parametric Vector Form is a mathematical representation of a vector in terms of parameters. It is commonly used in vector calculus and physics to describe the motion of objects in space.

2. How is Parametric Vector Form different from Cartesian Vector Form?

In Cartesian Vector Form, vectors are represented using their components in the x, y, and z directions. In Parametric Vector Form, vectors are represented using a parameter (usually denoted by t) that describes the magnitude and direction of the vector.

3. What is the significance of using parameters in Parametric Vector Form?

Using parameters allows for a more general representation of vectors, as it can describe vectors of any length and direction. It also makes it easier to manipulate and solve problems involving vectors, as the parameters can be treated as variables.

4. How is Parametric Vector Form used in physics?

In physics, Parametric Vector Form is used to describe the motion of objects in space. By assigning parameters to the position, velocity, and acceleration vectors, we can analyze and predict the motion of objects under the influence of forces.

5. Can Parametric Vector Form be used in higher dimensions?

Yes, Parametric Vector Form can be used to represent vectors in any number of dimensions. The number of parameters used will depend on the dimensionality of the vector. For example, a three-dimensional vector will require three parameters, while a two-dimensional vector will only require two parameters.

Similar threads

Evaluate the given integrals - line integrals
    • Calculus and Beyond Homework Help
Replies
2
Views
390
MHB -311.1.5.8 Ax=b in parametric vector form,
    • Linear and Abstract Algebra
Replies
7
Views
824
MHB 311.1.5.12 Ax=0 in parametric vector form
    • Linear and Abstract Algebra
Replies
7
Views
1K
Linear independence of Coordinate vectors as columns & rows
    • Calculus and Beyond Homework Help
Replies
2
Views
988
Solving ##y'' - 5 y' - 6y = e^{3x}## using Laplace Transform
    • Calculus and Beyond Homework Help
Replies
7
Views
789
Find the equation of the curve given: ##\frac{dy}{dx}=2(kx-1)^5##
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Prove 9 is eigenvalue of ##T^2\iff## 3 or -3 eigenvalue of ##T##.
    • Calculus and Beyond Homework Help
Replies
5
Views
526
Does there exist a 2x2 non-singular matrix with only one 1d eigenspace?
    • Calculus and Beyond Homework Help
Replies
2
Views
389
Why is this not a general solution to this nonlinear DE?
    • Calculus and Beyond Homework Help
Replies
5
Views
290
Which statements are true given a solution to the system x'=Ax?
    • Calculus and Beyond Homework Help
Replies
6
Views
1K

Hot Threads

Recent Insights

Back
Top