Finding k for Matrix: No Solutions, Infinite Solutions, Unique Solution

In summary, "k" in a matrix represents a constant value used in linear algebra and a matrix has no solution when its equations are contradictory. A matrix may have infinite solutions if there are more variables than equations, determined by its echelon form. A matrix cannot have both no solution and infinite solutions, only one or the other or a unique solution. The value of "k" in a matrix with a unique solution can be found using techniques such as row operations or Gaussian elimination.
  • #1
mr_coffee
1,629
1
OKay I'm trying to find a value of k in which this matrix is a) no solutions, b) infinite many solutions, and c) a unqiue solution, what do i do once i find the determinant? i used cramers rule:
http://img492.imageshack.us/img492/8854/lastscan4pp.jpg
THanks.
Oh yeah in the picture it should be the detZ/detA
 
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  • #2
n/m i got it, thanks!
 

FAQ: Finding k for Matrix: No Solutions, Infinite Solutions, Unique Solution

What is the significance of "k" in a matrix?

"k" in a matrix represents a constant value that is used in linear algebra to manipulate and solve equations.

What does it mean when a matrix has no solution?

A matrix has no solution when the equations it represents are contradictory or inconsistent, meaning there is no set of values that can satisfy all the equations simultaneously.

How can you determine if a matrix has infinite solutions?

If a matrix has more variables than equations, it is possible for there to be infinite solutions. This can be determined by reducing the matrix to its echelon form and identifying if there are any free variables.

Is it possible for a matrix to have both no solution and infinite solutions?

No, a matrix cannot have both no solution and infinite solutions. It can only have one or the other, or a unique solution.

How can you find the value of "k" in a matrix with a unique solution?

In a matrix with a unique solution, "k" can be found by using techniques such as row operations or Gaussian elimination to reduce the matrix to its reduced row echelon form. The value of "k" can then be determined by back substitution.

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