Matrix Problem with an Unknown quantity

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In summary, the conversation discusses finding the values of b that result in a system of equations having no unique solutions. The approach suggested is to use a "calculational" method, where the value of b is determined and then used to solve the system of equations. The key factor in determining the uniqueness of the solution is the rank of the matrix A, which can be found using mathematical software like MATLAB.
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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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  • #2
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?
 
  • #3
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)!
 

FAQ: Matrix Problem with an Unknown quantity

What is a matrix problem with an unknown quantity?

A matrix problem with an unknown quantity is a mathematical problem that involves a system of equations represented in matrix form, where one or more of the variables is unknown.

How do you solve a matrix problem with an unknown quantity?

To solve a matrix problem with an unknown quantity, you can use various methods such as Gaussian Elimination, Gauss-Jordan Elimination, or Cramer's Rule. These methods involve manipulating the equations in the matrix to isolate and solve for the unknown variable.

What are some real-world applications of matrix problems with an unknown quantity?

Matrix problems with an unknown quantity are commonly used in fields such as economics, engineering, and physics to model and solve complex systems. They can also be used in computer graphics, cryptography, and data analysis.

What are the limitations of solving a matrix problem with an unknown quantity?

The main limitation of solving a matrix problem with an unknown quantity is that it can be time-consuming and computationally intensive. In some cases, there may also be multiple solutions or no solutions at all, making it difficult to determine the correct answer.

How can I improve my skills in solving matrix problems with an unknown quantity?

To improve your skills in solving matrix problems with an unknown quantity, you can practice with various examples and exercises. You can also study different techniques and methods for solving these problems and seek help from teachers or online resources if needed.

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