document.write( "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? \r
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Algebra.Com's Answer #833509 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "For the given matrix, the values of h and k are real constants.
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document.write( "The corresponding matrix equation system is\r\n" );
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document.write( "    2x + 1y = h\r\n" );
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document.write( "    4x + ky = 0.\r\n" );
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document.write( "The determinant of the coefficient matrix is  d = 2k -4*1 = 2k - 4.\r\n" );
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document.write( "The determinant is zero if and only if d = 0 = 2k-4,  or  k = 2.\r\n" );
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document.write( "Case (a):  The system has infinite solutions if  k = 2  (meaning the determinant is zero)  and  h = 0.\r\n" );
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document.write( "Case (b):  The system has no solutions if  k = 2  (meaning the determinant is zero)  and  h =/= 0.\r\n" );
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document.write( "Case (c):  The system has a unique solution if  k =/= 2  (meaning the determinant is not zero).  \r\n" );
document.write( "                                                         In this case, there is no restrictions for h.\r\n" );
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