document.write( "Question 893904: Consider the following subspace of R^3:
\n" ); document.write( " W={(x,y,z)belong to R^3|2x+2y+z=0, 3x+3y-2z=0,x+y-3z=0}
\n" ); document.write( "The dimension of W is
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Algebra.Com's Answer #541777 by Fombitz(32388) $\"\"$ $\"About$

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$\"2x%2B2y%2Bz=0\"$
\n" ); document.write( " $\"3x%2B3y-2z=0\"$
\n" ); document.write( " $\"x%2By-3z=0\"$
\n" ); document.write( "Use row operations to show that rows 1 and 3 and rows 2 and 3 lead to $\"z=0\"$ .
\n" ); document.write( " $\"R%5B1%5D-2R%5B2%5D=0\"$
\n" ); document.write( " $\"R%5B2%5D-3R%5B3%5D=0\"$
\n" ); document.write( "That leaves you with
\n" ); document.write( " $\"x%2By=0\"$
\n" ); document.write( " $\"y=-x\"$
\n" ); document.write( "So only 1 independent choice of variables.
\n" ); document.write( " $\"dim%28W%29=1\"$
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