document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1037171>Question 1037171</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the following system of equations:<BR>\n" );
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document.write( "2x + 3y = 1<BR>\n" );
document.write( "5x + 9y = 4\r<BR>\n" );
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document.write( "(a) Write the system of equations as a matrix equation AX = B.<BR>\n" );
document.write( "(b) Calculate A<BR>\n" );
document.write( "&#8722;1<BR>\n" );
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document.write( "(c) Solve AX = B using your result from part (b). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #652590 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=652590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) The system <BR>\n" );
document.write( "2x + 3y = 1<BR>\n" );
document.write( "5x + 9y = 4<BR>\n" );
document.write( "is equivalent to the matrix equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C2%2C3%2C5%2C9%29%29%2A%28matrix%282%2C1%2Cx%2Cy%29%29+=+%28matrix%282%2C1%2C1%2C4%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%28matrix%282%2C2%2C2%2C3%2C5%2C9%29%29 ALIGN=MIDDLE  ALT=\"A+=+%28matrix%282%2C2%2C2%2C3%2C5%2C9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(b) The matrix <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%28matrix%282%2C2%2C2%2C3%2C5%2C9%29%29 ALIGN=MIDDLE  ALT=\"A+=+%28matrix%282%2C2%2C2%2C3%2C5%2C9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is nonsingular since its determinant is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18+-+15+=+3+%3C%3E+0 ALIGN=MIDDLE  ALT=\"18+-+15+=+3+%3C%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Its inverse is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E%28-1%29+=+%281%2F3%29%2A%28matrix%282%2C2%2C9%2C-3%2C-5%2C2%29%29 ALIGN=MIDDLE  ALT=\"A%5E%28-1%29+=+%281%2F3%29%2A%28matrix%282%2C2%2C9%2C-3%2C-5%2C2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C1%2Cx%2Cy%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C1%2Cx%2Cy%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%2A%28matrix%282%2C2%2C9%2C-3%2C-5%2C2%29%29%2A%28matrix%282%2C1%2C1%2C4%29%29 ALIGN=MIDDLE  ALT=\"%281%2F3%29%2A%28matrix%282%2C2%2C9%2C-3%2C-5%2C2%29%29%2A%28matrix%282%2C1%2C1%2C4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C1%2C-1%2C1%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C1%2C-1%2C1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after left-multiplying both sides of the equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E%28-1%29 ALIGN=MIDDLE  ALT=\"A%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplifying. </SPAN>\n" );
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