document.write( "Question 412059: I am not understanding how to Solve the system of linear equation using matrices\r
\n" ); document.write( "\n" ); document.write( "4x-y+2z=5
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\n" ); document.write( "\n" ); document.write( "Can you guide me step by step in solving it?\r
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Algebra.Com's Answer #289532 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "4x-y+2z=5\r\n" );
document.write( "  2y+z=4\r\n" );
document.write( "4x+y+3z=10\r\n" );
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document.write( " 4x-1y+2z =  5\r\n" );
document.write( " 0x+2y+1z =  4\r\n" );
document.write( " 4x+1y+3z = 10\r\n" );
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document.write( "Erase all the letters\r\n" );
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document.write( " 4 -1 +2 =  5\r\n" );
document.write( " 0 +2 +1 =  4\r\n" );
document.write( " 4 +1 +3 = 10\r\n" );
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document.write( "Erase all the + signs\r\n" );
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document.write( " 4 -1  2 =  5\r\n" );
document.write( " 0  2  1 =  4\r\n" );
document.write( " 4  1  3 = 10\r\n" );
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document.write( "Replace the equal signs with a |\r\n" );
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document.write( "⎾4 -1  2 |  5⏋\r\n" );
document.write( "⎢0  2  1 |  4⎢\r\n" );
document.write( "⎿4  1  3 | 10⏌\r\n" );
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document.write( "We want to end up with a matrix that looks like this:\r\n" );
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document.write( "⎾1  0  0 | ⎽⏋\r\n" );
document.write( "⎢0  1  0 | ⎽⎢\r\n" );
document.write( "⎿0  0  1 | ⎽⏌\r\n" );
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document.write( "-------------------------\r\n" );
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document.write( "First we get all the 0's\r\n" );
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document.write( "⎾4 -1  2 |  5⏋\r\n" );
document.write( "⎢0  2  1 |  4⎢\r\n" );
document.write( "⎿4  1  3 | 10⏌\r\n" );
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document.write( "To get a 0 where the 4 is on the lower left hand corner,\r\n" );
document.write( "multiply the top row by -1\r\n" );
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document.write( "⎾-4  1 -2 | -5⏋\r\n" );
document.write( "⎢ 0  2  1 |  4⎢\r\n" );
document.write( "⎿ 4  1  3 | 10⏌\r\n" );
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document.write( "Add the first row to the bottom row:\r\n" );
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document.write( "⎾-4  1 -2 | -5⏋\r\n" );
document.write( "⎢ 0  2  1 |  4⎢\r\n" );
document.write( "⎿ 0  2  1 |  5⏌\r\n" );
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document.write( "To get a 0 where the 1 is in the top row, multiply\r\n" );
document.write( "the top row by -2\r\n" );
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document.write( "⎾ 8 -2  4 | 10⏋\r\n" );
document.write( "⎢ 0  2  1 |  4⎢\r\n" );
document.write( "⎿ 0  2  1 |  5⏌\r\n" );
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document.write( "Add the middle row to the top row:\r\n" );
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document.write( "⎾ 8  0  5 | 14⏋\r\n" );
document.write( "⎢ 0  2  1 |  4⎢\r\n" );
document.write( "⎿ 0  2  1 |  5⏌\r\n" );
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document.write( "To get a 0 where the 2 on the bottom row is, multiply\r\n" );
document.write( "the bottom row by -1\r\n" );
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document.write( "⎾ 8  0  5 | 14⏋\r\n" );
document.write( "⎢ 0  2  1 |  4⎢\r\n" );
document.write( "⎿ 0 -2 -1 | -5⏌\r\n" );
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document.write( "Add the middle row to the bottom row\r\n" );
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document.write( "⎾ 8  0  5 | 14⏋\r\n" );
document.write( "⎢ 0  2  1 |  4⎢\r\n" );
document.write( "⎿ 0  0  0 | -1⏌\r\n" );
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document.write( "If you replace the letters now \r\n" );
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document.write( "  8x + 0y + 6z = 14\r\n" );
document.write( "  0x + 2y + 1z =  4\r\n" );
document.write( "  0x + 0y + 0z =  1\r\n" );
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document.write( "The bottom equation has no solution because the left\r\n" );
document.write( "side is 0 and the right side is 1, so there can be no\r\n" );
document.write( "solution.\r\n" );
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document.write( "Edwin
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