document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=950149>Question 950149</A>: <I><SPAN STYLE=\"word-break: break-all;\"> B= \r<BR>\n" );
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document.write( "1 2 3<BR>\n" );
document.write( "2 5 3<BR>\n" );
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document.write( "Find the inverse of Matrix B.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "Det(M)=<BR>\n" );
document.write( "40-26-15<BR>\n" );
document.write( "= -1<BR>\n" );
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document.write( "M11= 40<BR>\n" );
document.write( "M21= 13<BR>\n" );
document.write( "M31=-5\r<BR>\n" );
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document.write( "M12=16<BR>\n" );
document.write( "M22=5<BR>\n" );
document.write( "M32=-2\r<BR>\n" );
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document.write( "M13=-9<BR>\n" );
document.write( "M23=-3<BR>\n" );
document.write( "M33=1\r<BR>\n" );
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document.write( "40 16 -9     <BR>\n" );
document.write( "13  5 -3   <BR>\n" );
document.write( "-5 -2  1\r<BR>\n" );
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document.write( "+ - +<BR>\n" );
document.write( "- + -<BR>\n" );
document.write( "+ - +\r<BR>\n" );
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document.write( "40 -16 -9<BR>\n" );
document.write( "-13  5  3<BR>\n" );
document.write( "-5   2  1\r<BR>\n" );
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document.write( "M^-1=1/-1 \r<BR>\n" );
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document.write( "Brackets<BR>\n" );
document.write( "-40 16 9<BR>\n" );
document.write( "13 -5 -3 <BR>\n" );
document.write( "5  -2 -1<BR>\n" );
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document.write( "Did I do it right? Thanks in advance.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #580147 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=580147\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "yes, you did it right\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C1%2C2%2C3%2C2%2C+5+%2C3%2C1%2C0%2C8%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C1%2C2%2C3%2C2%2C+5+%2C3%2C1%2C0%2C8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "inverse\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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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_3x3_matrix.solver>Finding the Determinant of a 3x3 Matrix</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT><br>If you have the general 3x3 matrix:<br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2Ca%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2Ca%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><br>the <a  rel=nofollow HREF=\"http://en.wikipedia.org/wiki/Determinant#3-by-3_matrices\">determinant</a> is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%283%2C3%2Ca%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29%29=a%2Aabs%28matrix%282%2C2%2Ce%2Cf%2Ch%2Ci%29%29-b%2Aabs%28matrix%282%2C2%2Cd%2Cf%2Cg%2Ci%29%29%2Bc%2Aabs%28matrix%282%2C2%2Cd%2Ce%2Cg%2Ch%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><br>Which further breaks down to:<br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%283%2C3%2Ca%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29%29=a%28ei-fh%29-b%2A%28di-fg%29%2Bc%28dh-eg%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><br>Note: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%282%2C2%2Ce%2Cf%2Ch%2Ci%29%29 ALIGN=MIDDLE  ALT=\"abs%28matrix%282%2C2%2Ce%2Cf%2Ch%2Ci%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%282%2C2%2Cd%2Cf%2Cg%2Ci%29%29 ALIGN=MIDDLE  ALT=\"abs%28matrix%282%2C2%2Cd%2Cf%2Cg%2Ci%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%282%2C2%2Cd%2Ce%2Cg%2Ch%29%29 ALIGN=MIDDLE  ALT=\"abs%28matrix%282%2C2%2Cd%2Ce%2Cg%2Ch%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are determinants themselves.<br> If you need help finding the determinant of 2x2 matrices (which is <i>required</i> to find the determinant of 3x3 matrices), check out this <a  rel=nofollow HREF=\"http://www.algebra.com/algebra/homework/Matrices-and-determiminant/determinant-of-2x2-matrix.solver\">solver</a><br><br>--------------------------------------------------------------<br><br><br>From the matrix <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-40 ALIGN=MIDDLE  ALT=\"a=-40\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=16 ALIGN=MIDDLE  ALT=\"b=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=9 ALIGN=MIDDLE  ALT=\"c=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=13 ALIGN=MIDDLE  ALT=\"d=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e=-5 ALIGN=MIDDLE  ALT=\"e=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=-3 ALIGN=MIDDLE  ALT=\"f=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g=5 ALIGN=MIDDLE  ALT=\"g=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-2 ALIGN=MIDDLE  ALT=\"h=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i=-1 ALIGN=MIDDLE  ALT=\"i=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%283%2C3%2Ca%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29%29=a%28ei-fh%29-b%2A%28di-fg%29%2Bc%28dh-eg%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the general 3x3 determinant.<br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29=%28-40%29%28%28-5%29%28-1%29-%28-3%29%28-2%29%29-%2816%29%28%2813%29%28-1%29-%28-3%29%285%29%29%2B%289%29%28%2813%29%28-2%29-%28-5%29%285%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in the given values (see above)<br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29=%28-40%29%285-6%29-%2816%29%28-13--15%29%2B%289%29%28-26--25%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29=%28-40%29%28-1%29-%2816%29%282%29%2B%289%29%28-1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract<br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29=40-32%2B-9 ALIGN=MIDDLE  ALT=\"abs%28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29=40-32%2B-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29=-1 ALIGN=MIDDLE  ALT=\"abs%28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.<br><br><br>======================================================================<br><br><br>Answer:<br><br>So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29=-1 ALIGN=MIDDLE  ALT=\"abs%28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29=-1\"   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%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <font color=\"red\">-1</font><br></TD></TR>\n" );
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