Question 1199573
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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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<pre>
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.
</pre>

Solved and answered.