document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174766>Question 174766</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1602773033/algebrahomeworkh>Saxon Algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Find the inverse of \r<BR>\n" );
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document.write( "A= (matrix) -3....1<BR>\n" );
document.write( "                      -5....5\r<BR>\n" );
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document.write( "if it exists. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130140 by </B><A HREF=/tutors/aboutme.mpl?userid=KnightOwlTutor><B>KnightOwlTutor(293)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KnightOwlTutor><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=KnightOwlTutor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=130140\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We know that the matrix has an inverse because the determinant is not equal to zero\r<BR>\n" );
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document.write( "[-3 1]<BR>\n" );
document.write( "[-5 5]\r<BR>\n" );
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document.write( "[a  b]<BR>\n" );
document.write( "[c  d]\r<BR>\n" );
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document.write( "To calculate the determinant ad-bc in this case -15+5=-10\r<BR>\n" );
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document.write( "Any Matrix inverse =1/ad-bc[d -b]<BR>\n" );
document.write( "                           [-c a]\r<BR>\n" );
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document.write( "-1/10[5 -1]<BR>\n" );
document.write( "     [5 -3]\r<BR>\n" );
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document.write( "To double check multiply the matrices together and see if you come up with the identity matrix.\r<BR>\n" );
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document.write( "[-3 1]-1/10[5 -1]<BR>\n" );
document.write( "[-5 5]     [5  -3]\r<BR>\n" );
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document.write( "-15+5   3+3   -1/10[-10  0]\r<BR>\n" );
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document.write( "-25+25  5-15   -1/10[0  -10]\r<BR>\n" );
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document.write( "[1 0]<BR>\n" );
document.write( "[0 1] is the identity matrix\r<BR>\n" );
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document.write( " </SPAN>\n" );
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