Row Space, Column Space and Null Space

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SUMMARY

This discussion focuses on constructing a matrix whose null space is defined by the linear combinations of the vectors v1={1;-1;3;2} and v2={2;0;-2;4}. Additionally, it addresses the equation x1+x2+x3=1, which represents a linear system with three unknowns. The general solution is expressed as a combination of a particular solution and the general solution of the corresponding homogeneous system. Participants emphasize the importance of demonstrating effort in problem-solving rather than seeking direct answers.

PREREQUISITES
  • Understanding of linear algebra concepts such as null space and column space.
  • Familiarity with matrix construction and manipulation.
  • Knowledge of linear systems and homogeneous equations.
  • Ability to use LaTeX for mathematical expressions.
NEXT STEPS
  • Study the properties of null space and column space in linear algebra.
  • Learn how to construct matrices based on given vectors.
  • Explore methods for solving linear systems, including particular and homogeneous solutions.
  • Practice using LaTeX for formatting mathematical equations and expressions.
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Students and educators in mathematics, particularly those studying linear algebra, as well as anyone interested in enhancing their problem-solving skills in mathematical contexts.

Swati
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1.Construct a matrix whose null space consists of all linear combination of the vectors, v1={1;-1;3;2} and v2={2,0,-2,4} (v1,v2 are column vector).2.The equation x1+x2+x3=1 can be viewed as a linear system of one equation in three unknowns. Express its general solution as a particular solution plus the general solution of the corresponding homogeneous system.
 
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Swati said:
1.Construct a matrix whose null space consists of all linear combination of the vectors, v1={1;-1;3;2} and v2={2,0,-2,4} (v1,v2 are column vector).2.The equation x1+x2+x3=1 can be viewed as a linear system of one equation in three unknowns. Express its general solution as a particular solution plus the general solution of the corresponding homogeneous system.
Hello Swati.
Sorry but I can't answer your question.
Here at MHB helpers don't straightaway give you the solutions. We like to lead you to the solution and not blatantly provide the full solution. You are required to show some effort.. whatever ideas you had on how to approach your problem.
Also try to post using latex. To learn how to do that you can check out the latex help forum on the homepage.
Regards.
 

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