document.write( "Question 246519: Solve the system using augmented matrix. Show your work.\r
\n" ); document.write( "\n" ); document.write( "5x + 4y - z= 1
\n" ); document.write( "2x - 2y + z= 1
\n" ); document.write( "-x - y + z= 2\r
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Algebra.Com's Answer #180007 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve the system using augmented matrix. Show your work.\r
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document.write( "Write that as a matrix by dropping the letters\r\n" );
document.write( "and putting vertical line instead of equal signs:\r\n" );
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document.write( "The idea is to get three zeros in the three positions\r\n" );
document.write( "in the lower left corner of the matrix, where the elements\r\n" );
document.write( "I've colored red are:\r\n" );
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document.write( "To get a 0 where the red 2 is, multiply R3\r\n" );
document.write( "by 2 and add it to 1 times R2, and put it in place of the\r\n" );
document.write( "present R2.  That's written as\r\n" );
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document.write( "2R1+1R2->R2\r\n" );
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document.write( "To make it easy, write the multipliers to the left of the two\r\n" );
document.write( "rows you're working with; that is, put a 2 by R1 and a 1 by R2\r\n" );
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document.write( "We are going to change only R2.  Although R3 gets multiplied\r\n" );
document.write( "by 2 we are going to just do that mentally and add it to R2, but\r\n" );
document.write( "not really change R3.\r\n" );
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document.write( "-----\r\n" );
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document.write( "To get a 0 where the lower left red -1 is, multiply R1\r\n" );
document.write( "by 1 and add it to 5 times R3.  That's written as\r\n" );
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document.write( "1R1+5R3->R3\r\n" );
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document.write( "Write the multipliers to the left of the two rows you're \r\n" );
document.write( "working with; that is, put a 1 by R1 and a 5 by R3\r\n" );
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document.write( "We are going to change only R3. \r\n" );
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document.write( "To get a 0 where the remaining red -1 is, multiply R2\r\n" );
document.write( "by 1 and add it to -4 times R3.  That's written as\r\n" );
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document.write( "1R2-4R3->R3\r\n" );
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document.write( "Write the multipliers to the left of the two\r\n" );
document.write( "rows you're working with; that is, put a +1 by R2 and a -4 by R3\r\n" );
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document.write( "We are going to change only R3. \r\n" );
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document.write( "Now that we have 0's in the three positions in the\r\n" );
document.write( "lower left corner of the matrix, we change the matrix\r\n" );
document.write( "back to equations:\r\n" );
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document.write( "Solve the third equation for z:\r\n" );
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document.write( "Substitute 3 for z in the middle equation:\r\n" );
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document.write( "Substitute 3 for z and 1 for y in the top equation:\r\n" );
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document.write( "So the solution is \r\n" );
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document.write( "Edwin

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