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Question 1199573: For the given matrix, the values of h and k are real constants. For which value of h and k are there infinite solutions? no solutions? one solution?
[2 1 | h]
[4 k | 0]
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
For the given matrix, the values of h and k are real constants.
For which value of h and k are there (a) infinite solutions? (b) no solutions? (c) one solution?
[2 1 | h]
[4 k | 0]
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The corresponding matrix equation system is
2x + 1y = h
4x + ky = 0.
The determinant of the coefficient matrix is d = 2k -4*1 = 2k - 4.
The determinant is zero if and only if d = 0 = 2k-4, or k = 2.
Case (a): The system has infinite solutions if k = 2 (meaning the determinant is zero) and h = 0.
Case (b): The system has no solutions if k = 2 (meaning the determinant is zero) and h =/= 0.
Case (c): The system has a unique solution if k =/= 2 (meaning the determinant is not zero).
In this case, there is no restrictions for h.
Solved and answered.
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