document.write( "Question 22332: .7a + .25b + .3c = a
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Algebra.Com's Answer #11860 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
.7a + .25b + .3c = a\r\n" );
document.write( ".2a + .6b + .05c = b\r\n" );
document.write( ".1a + .15b + .65c = c\r\n" );
document.write( "WHERE a + b + c = 1\r\n" );
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document.write( "1st equation:     .7a + .25b +  .3c = a\r\n" );
document.write( "2nd equation:     .2a +  .6b + .05c = b\r\n" );
document.write( "3rd equation      .1a + .15b + .65c = c\r\n" );
document.write( "4th equation        a +    b    + c = 1\r\n" );
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document.write( "Subtract a, b, and c from both sides of the first three \r\n" );
document.write( "equations, respectively, and you have this system:\r\n" );
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document.write( "-.3a + .25b +  .3c = 0\r\n" );
document.write( " .2a -  .4b + .05c = 0\r\n" );
document.write( " .1a + .15b - .35c = 0\r\n" );
document.write( "   a +    b +    c = 0\r\n" );
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document.write( "The augmented matrix of this system is\r\n" );
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document.write( "[-.3   .25    .3 | 0]\r\n" );
document.write( "[ .2   -.4   .05 | 0]\r\n" );
document.write( "[ .1   .15  -.35 | 0]\r\n" );
document.write( "[  1     1     1 | 1]\r\n" );
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document.write( "which is row equivalent to its row reduced echelon form:\r\n" );
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document.write( "[1 0 0 53/111]\r\n" );
document.write( "[0 1 0  10/37]\r\n" );
document.write( "[0 0 1 28/111]\r\n" );
document.write( "[0 0 0   0   ]\r\n" );
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document.write( "a = 53/111\r\n" );
document.write( "b =  10/37\r\n" );
document.write( "c = 28/111\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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