document.write( "Question 1179823: Find all functions from {4, 5, 6} to {1, 2}. \n" ); document.write( "

Algebra.Com's Answer #809412 by ikleyn(52802) $\"\"$ $\"About$

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\n" ); document.write( "Find all functions from {4, 5, 6} to {1, 2}.
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\n" ); document.write( "\n" ); document.write( " This question may PERPLEX a beginning student.\r
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\n" ); document.write( "\n" ); document.write( " Do not worry: I will help you right now.\r
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document.write( "First, let me explain you how to represent each such function.\r\n" );
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document.write( "You may represent it as a  (2x3)-matrix with 2 rows and 3 columns.\r\n" );
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document.write( "The lower row of such matrix is  (4, 5, 6).\r\n" );
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document.write( "The upper row of such matrix contains the VALUES of the function at the points 4, 5 and 6.\r\n" );
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document.write( "For example, you may have such matrix\r\n" );
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document.write( "    A1 = .\r\n" );
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document.write( "It represents the function, which has value of 1 at 4; value of 1 at 5;  and value of 2  at 6.\r\n" );
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document.write( "Another matrix might be\r\n" );
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document.write( "    A2 = .\r\n" );
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document.write( "It represents the function, which has value of 2 at 4; value of 2 at 5;  and value of 1  at 6.\r\n" );
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document.write( "Each matrix with the upper row consisting of ones and twos, represents some function of this family;\r\n" );
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document.write( "all lower rows of these matrices are the same  (4, 5, 6).\r\n" );
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document.write( "The functions differ by their upper rows: different functions have different upper rows, constructed as described.\r\n" );
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document.write( "The total number of such matrices and such functions is   = 8,\r\n" );
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document.write( "because you may have any of the two values 1 or 2 in the upper row in each its position, independently.\r\n" );
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document.write( "If you are enthusiastic, you may write all these 8 matrices, if you want to assure yourself that you do understand my explanation and the idea.\r\n" );
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document.write( "I will not do it, saving the gray substance of my mind.\r\n" );
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document.write( "I hope my description/explanation is clear enough to you.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered, explained and completed.\r
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\n" ); document.write( "\n" ); document.write( "Do not forget to post your \"THANKS\" to me for my teaching.\r
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\n" ); document.write( "\n" ); document.write( "Based on this exposition, a poet of a major caliber would be able to write a poem or a song and perform it in YOUTUBE
\n" ); document.write( "gathering millions of subscribers.\r
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