document.write( "Question 360033: solve the system of equations by augmented matrix:
\n" ); document.write( "2x-y+z=1
\n" ); document.write( "x-y+z=-1
\n" ); document.write( "x-2y+z=2 \n" ); document.write( "
Algebra.Com's Answer #256900 by Jk22(389)\"\" \"About 
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Remark : (inspired by a comment)
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\n" ); document.write( "Note that the RHS is not linear but affine, hence different from eigenvalue-like problems (1x, -1y, 2z)*, hence the last column cannot be put on the in diagonal on the LHS :
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\n" ); document.write( "2 -1 +1 1 | -2last
\n" ); document.write( "1 -1 +1 -1 | -last
\n" ); document.write( "1 -2 +1 2
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\n" ); document.write( "0 3 -1 -3 | -3mid
\n" ); document.write( "0 1 0 -3
\n" ); document.write( "1 -2 1 2
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\n" ); document.write( "0 0 -1 6
\n" ); document.write( "0 1 0 -3
\n" ); document.write( "1 -2 1 2 | +2mid + first
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\n" ); document.write( "0 0 -1 6
\n" ); document.write( "0 1 0 -3
\n" ); document.write( "1 0 0 2
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\n" ); document.write( "=> x = 2, y = -3, z = -6
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\n" ); document.write( "Verification :
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\n" ); document.write( "2x-y+z = 4 + 3 - 6 = 7 - 6 = 1
\n" ); document.write( "x-y+z = 2 + 3 -6 = 5 - 6 = -1
\n" ); document.write( "x-2y+z = 2 + 6 -6 = 2 \n" ); document.write( "
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