document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129197>Question 1129197</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the determinant of the matrix. Determine whether the matrix has an inverse, but don't calculate the inverse.\r<BR>\n" );
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document.write( "[2 1 0]<BR>\n" );
document.write( "[0 -2 4]<BR>\n" );
document.write( "[0 1 -3]\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 #745760 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=745760\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C3%2Ca%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C3%2Ca%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The determinant is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+a%28ei+-+fh%29+-b%28di+-+fg%29+%2B+c%28dh+-eg%29 ALIGN=MIDDLE  ALT=\"D+=+a%28ei+-+fh%29+-b%28di+-+fg%29+%2B+c%28dh+-eg%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C3%2C2%2C+1%2C+0%2C%0D%0A0%2C+-2%2C+4%2C%0D%0A0+%2C1%2C+-3%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C3%2C2%2C+1%2C+0%2C%0D%0A0%2C+-2%2C+4%2C%0D%0A0+%2C1%2C+-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+2%28-2%2A%28-3%29+-+4%2A1%29+-+1%280%2A%28-3%29+-4%2A0%29+%2B+0%280%2A1+-+%28-2%29%2A0%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+2%286+-+4%29+-+1%280%2A0%29+%2B+0%280%29 ALIGN=MIDDLE  ALT=\"D+=+2%286+-+4%29+-+1%280%2A0%29+%2B+0%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+2%282%29 ALIGN=MIDDLE  ALT=\"D+=+2%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+4 ALIGN=MIDDLE  ALT=\"D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the matrix <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C3%2C2%2C+1%2C+0%2C%0D%0A0%2C+-2%2C+4%2C%0D%0A0+%2C1%2C+-3%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C3%2C2%2C+1%2C+0%2C%0D%0A0%2C+-2%2C+4%2C%0D%0A0+%2C1%2C+-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  have inverse because D = 4\r<BR>\n" );
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document.write( "If the determinant of the matrix is zero, then it will not have an inverse; the matrix is then said to be singular. Only non-singular matrices have inverses.\r<BR>\n" );
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