document.write( "Question 1164525: Find the values of x, y, and z so that matrix A =\r
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Algebra.Com's Answer #789178 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
A square matrix is Invertible if and only if its determinant is non-zero.\r\n" );
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document.write( "\"%28matrix%283%2C3%2C%0D%0A1%2C+2%2C+x%2C%0D%0A3%2C+0%2C+y%2C%0D%0A1%2C+1%2C+z%29%29\"\r\n" );
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document.write( "We find its determinant\r\n" );
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document.write( "\"abs%28matrix%283%2C3%2C%0D%0A1%2C+2%2C+x%2C%0D%0A3%2C+0%2C+y%2C%0D%0A1%2C+1%2C+z%29%29\"\"%22%22=%22%22\"\"1%2A0%2Az%2B2%2Ay%2A1%2Bx%2A3%2A1-x%2A0%2A1-2%2A3%2Az-1%2Ay%2A1\"\"%22%22=%22%22\"\"0%2B2y%2B3x-0-6z-y\"\"%22%22=%22%22\"\"3x%2By-6z\"\r\n" );
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document.write( "We can choose any values for x, y, z such that \r\n" );
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document.write( "\"3x%2By-6z%3C%3E0\"\r\n" );
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document.write( "I'll arbitrary choose x=3, y=-2, z=1 (to make the determinant 1, so its\r\n" );
document.write( "inverse will have all integer elements:\r\n" );
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document.write( "\"%28matrix%283%2C3%2C%0D%0A1%2C+2%2C+3%2C%0D%0A3%2C+0%2C+-2%2C%0D%0A1%2C+1%2C+1%29%29\"\r\n" );
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document.write( "Then its inverse is\r\n" );
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document.write( "\"%28matrix%283%2C3%2C%0D%0A2%2C+1%2C+-4%2C%0D%0A-5%2C+-2%2C+1%2C%0D%0A3%2C+1%2C+-6%29%29\"\r\n" );
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document.write( "Edwin
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