document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=22329>Question 22329</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Im really stuck! Show that the set S= 2X2 matrx (a 0 (1st row) and 0 b (2nd row)) is a subspace of the vector space of ALL 2X2 matrices.  Give basis for S.  What is the dimension of S?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #10860 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=10860\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  S= 2X2 matrx (a 0 (1st row) and 0 b (2nd row)) is a subspace of the vector space of ALL 2X2 matrices. Give basis for S. What is the dimension of S? <BR>\n" );
document.write( " (a 0)<BR>\n" );
document.write( " (0 b)\r<BR>\n" );
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document.write( " Note that the set all 2x2  matrices (say over R) is <BR>\n" );
document.write( " a v.s. of dim 2x2 = 4.(why ?)\r<BR>\n" );
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document.write( " Now, S contains two indep. matrices<BR>\n" );
document.write( " (1 0)<BR>\n" );
document.write( " (0 0) and\r<BR>\n" );
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document.write( " (0 0)<BR>\n" );
document.write( " (0 1)<BR>\n" );
document.write( " they form a basis of S and dim S = 2 (why ?)\r<BR>\n" );
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document.write( " Kenny\r<BR>\n" );
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document.write( " </SPAN>\n" );
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