document.write( "Question 116336This question is from textbook college algebra
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\n" ); document.write( "problem 1.)2x + y - 3z =1
\n" ); document.write( " 3x - y + 4z =6
\n" ); document.write( " x + 2y - z =9
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Algebra.Com's Answer #84592 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
I need help with these two matrice problems- solving it by the Gaussian elimination method:
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document.write( "2x + 1y - 3z = 1 \r\n" );
document.write( "3x - 1y + 4z = 6 \r\n" );
document.write( "1x + 2y - 1z = 9\r\n" );
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document.write( "Abbreviate this with an augmented matrix:\r\n" );
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document.write( "[2   1  -3  | 1] \r\n" );
document.write( "[3  -1   4  | 6] \r\n" );
document.write( "[1   2  -1  | 9]\r\n" );
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document.write( "Get a zero where the 3 is by\r\n" );
document.write( "multiplying the top row by -3,\r\n" );
document.write( "and the middle row by 2:\r\n" );
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document.write( "[-6   -3   9  | -3] \r\n" );
document.write( "[ 6   -2   8  | 12] \r\n" );
document.write( "[ 1    2  -1  |  9]\r\n" );
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document.write( "Add the top row to the middle row:\r\n" );
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document.write( "[-6   -3   9  | -3] \r\n" );
document.write( "[ 0   -5  17  |  9] \r\n" );
document.write( "[ 1    2  -1  |  9]\r\n" );
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document.write( "Get a zero where the 1 is by\r\n" );
document.write( "multiplying the top row by 1,\r\n" );
document.write( "and the bottom row by 6:\r\n" );
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document.write( "[-6   -3   9  | -3] \r\n" );
document.write( "[ 0   -5  17  |  9] \r\n" );
document.write( "[ 6   12  -6  | 54]\r\n" );
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document.write( "Add the top row to the bottom row:\r\n" );
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document.write( "[-6   -3   9  | -3] \r\n" );
document.write( "[ 0   -5  17  |  9] \r\n" );
document.write( "[ 0    9   3  | 51]\r\n" );
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document.write( "Get a zero where the 9 is on\r\n" );
document.write( "the bottom row by multiplying \r\n" );
document.write( "the middle row by 9,\r\n" );
document.write( "and the bottom row by 5:\r\n" );
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document.write( "[-6   -3   9  |  -3] \r\n" );
document.write( "[ 0  -45 153  |  81] \r\n" );
document.write( "[ 0   45  15  | 255]\r\n" );
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document.write( "Add the middle row to the bottom row:\r\n" );
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document.write( "[-6   -3   9  |  -3] \r\n" );
document.write( "[ 0  -45 153  |  81] \r\n" );
document.write( "[ 0    0 168  | 336]\r\n" );
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document.write( "Rewrite as a new system of equations:\r\n" );
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document.write( " -6x - 3y +   9z =  -3 \r\n" );
document.write( "     -45y + 153z =  81 \r\n" );
document.write( "            168z = 336\r\n" );
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document.write( "Solve the bottom equation for z:\r\n" );
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document.write( "            168z = 336\r\n" );
document.write( "               z = \"336%2F168\"\r\n" );
document.write( "               z = 2 \r\n" );
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document.write( "Substitute z = 2 in the middle equation \r\n" );
document.write( "and solve for y:\r\n" );
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document.write( "     -45y + 153z = 81\r\n" );
document.write( "   -45y + 153(2) = 81\r\n" );
document.write( "      -45y + 306 = 81\r\n" );
document.write( "            -45y = -225       \r\n" );
document.write( "               y = \"%28-255%29%2F%28-45%29\" \r\n" );
document.write( "               y = 5\r\n" );
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document.write( "Substitute y = 5 and z = 2 in the top equation \r\n" );
document.write( "and solve for x:\r\n" );
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document.write( "    -6x - 3y + 9z = -3\r\n" );
document.write( "-6x - 3(5) + 9(2) = -3\r\n" );
document.write( "    -6x - 15 + 18 = -3\r\n" );
document.write( "          -6x + 3 = -3\r\n" );
document.write( "              -6x = -6\r\n" );
document.write( "                x = \"%28-6%29%2F%28-6%29\"\r\n" );
document.write( "                x = 1\r\n" );
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document.write( "So the solution is (x, y, z) = (1, 5, 2)\r\n" );
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document.write( "Edwin
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