document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=4520>Question 4520</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let A be an m x n matrix. Prove that if B can be obtained from A by an elementary row (column) operation, then B transpose can be obtained from <BR>\n" );
document.write( "A transpose by the corresponding elementary column (row) operation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #2067 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=2067\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">   Proof: If B = EA, where E is a matrix of an elementary row (column) operation,<BR>\n" );
document.write( "        then transpose of B, B^T = (EA)^T = A^TE^T .<BR>\n" );
document.write( "        Since the transpose of a row(column) operation is a column(row) operation.<BR>\n" );
document.write( "        we see that E^T will be a matrix of an elementary column (row) operation,  <BR>\n" );
document.write( "        B transpose can be obtained from A transpose by the corresponding elementary column (row) operation.<BR>\n" );
document.write( " <BR>\n" );
document.write( " Kenny </SPAN>\n" );
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