SOLUTION: Determine the values ​​of K for which the following system has a nonzero solution: Kx + Ky = 0 4x + 2Ky = 0 The official answer is K=0 and K=2 but I don't know

Algebra ->  Matrices-and-determiminant -> SOLUTION: Determine the values ​​of K for which the following system has a nonzero solution: Kx + Ky = 0 4x + 2Ky = 0 The official answer is K=0 and K=2 but I don't know       Log On


   

Question 549766: Determine the values ​​of K for which the following system has a nonzero solution:
Kx + Ky = 0 4x + 2Ky = 0
The official answer is K=0 and K=2 but I don't know how to do this. Help me please!
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


You have worded the question incorrectly because if or then the given system is either consistent/dependent (same line) or inconsistent (parallel lines).

Calculate the determinant:



If the determinant is zero, then the system is either consistent/dependent (same line) or inconsistent (parallel lines).






or



So or yields no unique solution.

In fact, the set of values of for which your system yields a unique solution is all real numbers EXCEPT 0 and 2. Note, however, that the unique solution is, in every case, the origin

John

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