Matrix Problem with an Unknown quantity

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SUMMARY

The discussion centers on determining values of b in the matrix equation y = Cx, where C is a 4x4 matrix. The user seeks to identify conditions under which the system does not yield a unique solution. It is established that a unique solution exists when the rank of matrix A, denoted as r(A), equals the number of variables n. The user primarily utilizes MATLAB for calculations and is looking for methods to compute r(A).

PREREQUISITES
  • Understanding of matrix rank and its implications on solution uniqueness
  • Familiarity with MATLAB for matrix computations
  • Knowledge of linear algebra concepts, specifically systems of linear equations
  • Ability to perform matrix operations and manipulations
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  • Learn how to compute the rank of a matrix in MATLAB using the rank() function
  • Study the implications of the rank-nullity theorem in linear algebra
  • Explore methods for determining the conditions for unique solutions in linear systems
  • Investigate the use of the Reduced Row Echelon Form (RREF) to analyze matrix solutions
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Students and professionals in mathematics, engineers working with linear systems, and anyone using MATLAB for solving matrix equations will benefit from this discussion.

blackbear
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I have the following matrix, C =

3 2 1 9
4 2 6 12
1 4 -3 3
0 1 8 (3-b)

y1=[-1 -1 1 -1] transpose

For the vector y, I need to find all values of b such that the system of equations y=Cx has no unique solutions. Can someone help...

Thanks
 
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Perhaps the easiest approach is a "calculational" one... Suppose that a value for b was given. Then how would you go about solving y = Cx. At what point would you be able to tell if there was a unique solution?
 
I do the problems mostly with mathlab. Anyway, when rank r(A) equals n then there exist a unique solution. But I don't know how to find r(A)!
 

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