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

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SUMMARY

The discussion centers on determining the value of k for a matrix to achieve three conditions: no solutions, infinite solutions, and a unique solution. The user references Cramer's Rule and the relationship between the determinants of matrices, specifically detZ and detA. The key takeaway is that the determinant must equal zero for infinite solutions or no solutions, while a non-zero determinant indicates a unique solution.

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mr_coffee
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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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n/m i got it, thanks!
 

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