document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1031370>Question 1031370</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me with this::<BR>\n" );
document.write( "is this statement true or false : matrix B & C are equivalent <BR>\n" );
document.write( "matrix B =<BR>\n" );
document.write( "(<BR>\n" );
document.write( "matrix( 3, 4,<BR>\n" );
document.write( "1, 3, -2, 2,<BR>\n" );
document.write( "-1, -2, -1, -1,<BR>\n" );
document.write( "-1, -5, 8, -3,<BR>\n" );
document.write( ")<BR>\n" );
document.write( ")<BR>\n" );
document.write( "and matrix C=<BR>\n" );
document.write( "(<BR>\n" );
document.write( "matrix( 3,4,<BR>\n" );
document.write( "1, 2, 1, 2,<BR>\n" );
document.write( "1, 1, 4, 0,<BR>\n" );
document.write( "1, -1, -4, 1,<BR>\n" );
document.write( ")<BR>\n" );
document.write( ") </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #646108 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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/cgi-bin/show-face.mpl?user=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=646108\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Matrix B can be shown to be row-equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C1%2C0%2C-7%2C0%2C0%2C1%2C-3%2C1%2C0%2C0%2C0%2C1%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C4%2C1%2C0%2C-7%2C0%2C0%2C1%2C-3%2C1%2C0%2C0%2C0%2C1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  A few more column operations would lead to equivalence to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C1%2C0%2C0%2C0%2C0%2C1%2C0%2C0%2C0%2C0%2C1%2C0%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C4%2C1%2C0%2C0%2C0%2C0%2C1%2C0%2C0%2C0%2C0%2C1%2C0%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "By performing a sequence of row operations and then a sequence of column operations, matrix <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+%28matrix%28+3%2C4%2C%0D%0A1%2C+2%2C+1%2C+2%2C%0D%0A1%2C+1%2C+4%2C+0%2C%0D%0A1%2C+-1%2C+-4%2C+1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > can also be shown to be equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C1%2C0%2C0%2C0%2C0%2C1%2C0%2C0%2C0%2C0%2C1%2C0%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C4%2C1%2C0%2C0%2C0%2C0%2C1%2C0%2C0%2C0%2C0%2C1%2C0%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Therefore matrices B and C are equivalent to the same row- and column-reduced matrix, and so they themselves are equivalent to each other. </SPAN>\n" );
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