document.write( "Question 29492: Let U and V be subspaces of Rn. Prove that the intersection, U n V, is also a subspace of Rn. \n" ); document.write( "

Algebra.Com's Answer #17290 by venugopalramana(3286) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let U and V be subspaces of Rn. Prove that the intersection, U n V, is also a subspace of Rn.
\n" ); document.write( "LET US USE THE FOLLOWING SYMBOLS...E TO SHOW ELEMENT OF.
\n" ); document.write( "LET U INTERSECTION V = W
\n" ); document.write( "1.0 E U AND 0 E V...SO 0 E W...SO W IS NOT EMPTY.
\n" ); document.write( "2.LET A,B BE ELEMENTS OF W AND X,Y BE SCALAR ELEMENTS IN THE FIELD OF RN.
\n" ); document.write( "3.THE ABOVE IMPLIES THAT A,B ARE ELEMENTS OF U .HENCE XA+YB IS AN ELEMENT OF U.
\n" ); document.write( "4.SIMILARLY.......XA+YB IS AN ELEMENT OF V.
\n" ); document.write( "5.HENCE XA+YB IS AN ELEMENT OF W.
\n" ); document.write( "6.THUS WE SHOWED THAT IF A,B ARE ELEMENTS OF W AND X,Y ARE ANY SCALARS IN THE FIELD OF RN THEN X+YB IS AN ELEMENT OF W.
\n" ); document.write( "7.HENCE W IS A SUBSPACE OF RN. \n" ); document.write( "

\n" );