document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129205>Question 1129205</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the inverse of each matrix if it exists:<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 #745786 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=745786\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your matrix\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C2%2C3%2C7%2C1%2C-4%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C2%2C3%2C7%2C1%2C-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "first make sure determinant is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > zero\r<BR>\n" );
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document.write( "&#916; = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%28-4%29-7%2A1 ALIGN=MIDDLE  ALT=\"3%2A%28-4%29-7%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "&#916; =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-12-7 ALIGN=MIDDLE  ALT=\"+-12-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "&#916; = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-19 ALIGN=MIDDLE  ALT=\"-19\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, determinant is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > zero, therefore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=inverse ALIGN=MIDDLE  ALT=\"inverse\"   DISABLED_style= \"max-width:90%; height:auto;\" > matrix <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=exists ALIGN=MIDDLE  ALT=\"exists\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Write the augmented matrix:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C4%2C3%2C%097%2C%091%2C%090%2C%0D%0A1%2C%09-4%2C%090%2C%091%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C4%2C3%2C%097%2C%091%2C%090%2C%0D%0A1%2C%09-4%2C%090%2C%091%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find the pivot in the 1st column and swap the 2nd and the 1st rows:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C4%2C1%2C%09-4%2C%090%2C%091%2C%0D%0A3%2C%097%2C%091%2C%090%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C4%2C1%2C%09-4%2C%090%2C%091%2C%0D%0A3%2C%097%2C%091%2C%090%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Eliminate the 1st column:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C4%2C1%2C%09-4%2C%090%2C%091%2C%0D%0A0%2C%0919%2C%091%2C%09-3%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C4%2C1%2C%09-4%2C%090%2C%091%2C%0D%0A0%2C%0919%2C%091%2C%09-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Make the pivot in the 2nd column by dividing the 2nd row by 19:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C4%2C1%2C%09-4%2C%090%2C%091%2C%0D%0A0%2C%091%2C%091%2F19%2C%09-3%2F19%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C4%2C1%2C%09-4%2C%090%2C%091%2C%0D%0A0%2C%091%2C%091%2F19%2C%09-3%2F19%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Eliminate the 2nd column:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C4%2C%0D%0A1%2C%090%2C%094%2F19%2C%097%2F19%2C%0D%0A0%2C%091%2C%091%2F19%2C%09-3%2F19%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "There is the inverse matrix on the right:\r<BR>\n" );
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document.write( "Eliminate the 2nd column:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C4%2C%0D%0A1%2C%090%2C%09highlight%284%2F19%29%2C%09highlight%287%2F19%29%2C%0D%0A0%2C%091%2C%09highlight%281%2F19%29%2C%09highlight%28-3%2F19%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Result:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C2%2C%0D%0A4%2F19%2C7%2F19%2C%0D%0A1%2F19%2C-3%2F19%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C2%2C%0D%0A4%2F19%2C7%2F19%2C%0D%0A1%2F19%2C-3%2F19%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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