document.write( "Question 846536: Let x, y, and z be vectors in a vector space V.
\n" ); document.write( "Prove that if:
\n" ); document.write( "x + y = x + z
\n" ); document.write( "then y = z. \n" ); document.write( "

Algebra.Com's Answer #509779 by Fombitz(32388) $\"\"$ $\"About$

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In the vector space there exists a vector xi such that when added to vector x, you will get the zero vector.
\n" ); document.write( "Add xi to both sides.
\n" ); document.write( "x+y+xi=x+z+xi
\n" ); document.write( "Since addition is commutative,
\n" ); document.write( "x+xi+y=x+xi+z
\n" ); document.write( "0+y=0+z
\n" ); document.write( "By identity,
\n" ); document.write( "y=z \n" ); document.write( "

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