document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=940542>Question 940542</A>: <I><SPAN STYLE=\"word-break: break-all;\"> steps and solution how to solve this question:<BR>\n" );
document.write( "M is the matrix (3 4)<BR>\n" );
document.write( "                (p q)<BR>\n" );
document.write( " If M is a singular matrix and p=2,calculate the value of q.    </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #573209 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=573209\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> M is the matrix \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M=%28matrix%282%2C2%2C3%2C4%2Cp%2Cq%29%29 ALIGN=MIDDLE  ALT=\"M=%28matrix%282%2C2%2C3%2C4%2Cp%2Cq%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M ALIGN=MIDDLE  ALT=\"M\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a singular matrix and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2 ALIGN=MIDDLE  ALT=\"p=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,calculate the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q ALIGN=MIDDLE  ALT=\"q\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "\n" );
document.write( "A square matrix which does not have an inverse. A matrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=singular ALIGN=MIDDLE  ALT=\"singular\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=if ALIGN=MIDDLE  ALT=\"if\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=only ALIGN=MIDDLE  ALT=\"only\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=if ALIGN=MIDDLE  ALT=\"if\"   DISABLED_style= \"max-width:90%; height:auto;\" > its <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=determinant ALIGN=MIDDLE  ALT=\"determinant\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zero ALIGN=MIDDLE  ALT=\"zero\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "so,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=3q-4p=0 ALIGN=MIDDLE  ALT=\"D=3q-4p=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2 ALIGN=MIDDLE  ALT=\"p=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3q-4%2A2=0 ALIGN=MIDDLE  ALT=\"3q-4%2A2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3q-8=0 ALIGN=MIDDLE  ALT=\"3q-8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3q=8 ALIGN=MIDDLE  ALT=\"3q=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=8%2F3 ALIGN=MIDDLE  ALT=\"q=8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "check:\r<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=determinant_of_2x2_matrix.solver>Finding the Determinant of a 2x2 Matrix</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT><br>If you have the general 2x2 matrix:<br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><br>the <a  rel=nofollow HREF=\"http://en.wikipedia.org/wiki/Determinant#2-by-2_matrices\">determinant</a> is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=a%2Ad-c%2Ab ALIGN=MIDDLE  ALT=\"D=a%2Ad-c%2Ab\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><br>So this means that <br> <br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29=a%2Ad-c%2Ab ALIGN=MIDDLE  ALT=\"abs%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29=a%2Ad-c%2Ab\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><br>Note: the vertical bars denote a determinant.<br><br><br>-----------------------------------------------------------------<br><br><br>So in this case the determinant of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C3%2C4%2C2%2C8%2F3%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C3%2C4%2C2%2C8%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is:<br><BR>\n" );
document.write( "  <br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%282%2C2%2C3%2C4%2C2%2C8%2F3%29%29=%283%29%288%2F3%29-%282%29%284%29=8-8=0 ALIGN=MIDDLE  ALT=\"abs%28matrix%282%2C2%2C3%2C4%2C2%2C8%2F3%29%29=%283%29%288%2F3%29-%282%29%284%29=8-8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <br><br>Note: if you are having trouble with the fractions, check out this <a  rel=nofollow HREF=\"http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver\">solver</a><br><br><br>======================================================<br><br><br>Answer:<br><br>So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%282%2C2%2C3%2C4%2C2%2C8%2F3%29%29=0 ALIGN=MIDDLE  ALT=\"abs%28matrix%282%2C2%2C3%2C4%2C2%2C8%2F3%29%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that the determinant of the matrix <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C3%2C4%2C2%2C8%2F3%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C3%2C4%2C2%2C8%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <font color=\"red\">0</font><br></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );