document.write( "Question 168726: Solve the system by using an augmented matrix.
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Algebra.Com's Answer #124438 by Edwin McCravy(20060) $\"\"$ $\"About$

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Solve the system by using an augmented matrix.
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document.write( "We need to end up with a matrix that looks like this:\r\n" );
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document.write( "Plan: by using row operations,\r\n" );
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document.write( "1. get a 0 on the left of the 2nd row.\r\n" );
document.write( "2. get a 0 in the middle in the 1st row.\r\n" );
document.write( "3. get a 1 on the left of the 1st row.\r\n" );
document.write( "4. get a 1 in the middle of the 2nd row.\r\n" );
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document.write( "Also, any time a row can be easily divided through\r\n" );
document.write( "by a constant, we will stop and do that too:\r\n" );
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document.write( "To get a 0 where the 3 is, we mentally multiply\r\n" );
document.write( "each member of the first row by -3 and mentally\r\n" );
document.write( "add it to 5 time the corresponding number and\r\n" );
document.write( "replace the number in the second row by what\r\n" );
document.write( "we get.  To make it easy to do this mentally,\r\n" );
document.write( "be sure to write -3 to the left of the 1st row\r\n" );
document.write( "and 5 to the left ofthe 2nd row, so we can\r\n" );
document.write( "easily do the work mentally:\r\n" );
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document.write( "Notice that the second row can be divided through by -13,\r\n" );
document.write( "so we stop and do that:\r\n" );
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document.write( "To get a 0 where the 1 in the middle on the top\r\n" );
document.write( "row is, we mentally multiply each member of the \r\n" );
document.write( "2nd row by -1 and mentally add it to 1 times the \r\n" );
document.write( "corresponding number and replace the number in \r\n" );
document.write( "the first row by what we get.  To make it easy \r\n" );
document.write( "to do this mentally, be sure to write -1 to the \r\n" );
document.write( "left of the 2nd row and 1 to the left of the 1st\r\n" );
document.write( "row, so we can easily do the work mentally:\r\n" );
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document.write( "Now we just need to get a 1 where the 5 is. So\r\n" );
document.write( "we divide the 1st row through by 5:\r\n" );
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document.write( "Now we interpret the matrix\r\n" );
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document.write( "as the sytem of equations:\r\n" );
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document.write( "or just\r\n" );
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document.write( "Edwin

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