document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1160480>Question 1160480</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Perform the sequence of row operations on the matrix.<BR>\n" );
document.write( "(a)SwapR1 andR3.<BR>\n" );
document.write( "(b) Replace R2 by R2 plus -5 times R1.<BR>\n" );
document.write( "(C) Replace R3 by R3 plus -3 times R1.<BR>\n" );
document.write( "The matrix is <BR>\n" );
document.write( "3 -10 -2<BR>\n" );
document.write( "5 1 5<BR>\n" );
document.write( "1 6 -1\r<BR>\n" );
document.write( "\n" );
document.write( "The possible answers are <BR>\n" );
document.write( "(A) <BR>\n" );
document.write( "1 6 -1<BR>\n" );
document.write( "0 -29 10<BR>\n" );
document.write( "0 -28 1\r<BR>\n" );
document.write( "\n" );
document.write( "(B)<BR>\n" );
document.write( "1 5 -3<BR>\n" );
document.write( "0 -17 8<BR>\n" );
document.write( "0 -40 3\r<BR>\n" );
document.write( "\n" );
document.write( "(C)<BR>\n" );
document.write( "7 6 -7<BR>\n" );
document.write( "-3 -28 1<BR>\n" );
document.write( "-8 -29 10\r<BR>\n" );
document.write( "\n" );
document.write( "(D)<BR>\n" );
document.write( "7 6 -7<BR>\n" );
document.write( "-3 -40 3<BR>\n" );
document.write( "-8 -17 8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #783747 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=783747\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "What is it about this that you need help with?<br><BR>\n" );
document.write( "Simply do what it tells you to do and see what you end up with.<br><BR>\n" );
document.write( "In case you don't understand what it is they are asking you to do, I will get you started.<br><BR>\n" );
document.write( "The original matrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C3%2C3%2C-10%2C-2%2C5%2C1%2C5%2C1%2C6%2C-1%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C3%2C3%2C-10%2C-2%2C5%2C1%2C5%2C1%2C6%2C-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(a)Swap R1 and R3<br><BR>\n" );
document.write( "This says switch rows 1 and 3.  That will give you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C3%2C1%2C6%2C-1%2C5%2C1%2C5%2C3%2C-10%2C-2%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C3%2C1%2C6%2C-1%2C5%2C1%2C5%2C3%2C-10%2C-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(b) Replace R2 by R2 plus -5 times R1<br><BR>\n" );
document.write( "This says replace row 2 with row 2 plus (-5) times row 1.<br><PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "            row 2:   5   1  5\r\n" );
document.write( "   -5 times row 1:  -5 -30  5\r\n" );
document.write( "          -------------------\r\n" );
document.write( "        new row 2:   0 -29 10</PRE><BR>\n" );
document.write( "The matrix is now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C3%2C1%2C6%2C-1%2C0%2C-29%2C10%2C3%2C-10%2C-2%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C3%2C1%2C6%2C-1%2C0%2C-29%2C10%2C3%2C-10%2C-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(c) Replace R3 by R3 plus -3 times R1<br><BR>\n" );
document.write( "Similar to step (b), replace row 3 with row 3 plus (-3) times row 1.<br><BR>\n" );
document.write( "I'll let you do that step, in the same way as shown above for step (b).<br><BR>\n" );
document.write( "Step (c) does not change row 1 of the matrix, and only answer choice A has the correct first row, so that has to be the right answer.<br><BR>\n" );
document.write( "You can complete the details of step (c) to verify that answer A is correct.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );