document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1050415>Question 1050415</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I'm having trouble with this question. I don't know how I'm supposed to work it out, so any help would be great appreciated! Thank you! <BR>\n" );
document.write( "Determine the values for \"a\" for which the following system of linear equations has no solutions, a unique solution, or infinitely many solutions. I need to solve using a matrix, and then row reducing. <BR>\n" );
document.write( "3X1 + aX2 + 6X3 = 6<BR>\n" );
document.write( "-X1 + 3X2 - X3 = 1<BR>\n" );
document.write( "2X1 - 2X2 + 6X3 = 11  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #665970 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=665970\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Determine the values for \"a\" for which the following system of linear equations has no solutions, a unique solution, or infinitely many solutions. I need to solve using a matrix, and then row reducing. <BR>\n" );
document.write( "3X1 + aX2 + 6X3 = 6<BR>\n" );
document.write( "-X1 + 3X2 - X3 = 1<BR>\n" );
document.write( "2X1 - 2X2 + 6X3 = 11 <BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "You have to find the determinant of the \"coefficient matrix\"::<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "D = (3*3*6 + (-1*2*6) + (2*-1*a) - [(6*3*2)+(-1*-2*3)+(6*-1*a))<BR>\n" );
document.write( "----<BR>\n" );
document.write( "D = (54 - 12 - 2a - [36 + 6 - 6a])<BR>\n" );
document.write( "----<BR>\n" );
document.write( "D = (42-2a)-(42-6a)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "D = 4a<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "One unique solution if a is not zero<BR>\n" );
document.write( "No solution when a = 0<BR>\n" );
document.write( "----<BR>\n" );
document.write( "I'll leave the row reducing to you.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );