Inverse matrices | Clipmarks


	Inverse matrices
coburgmaths
9-14-2009 4:43 AM
238 views
coburgmaths says:
Some theory on finding the inverse of a 2x2 matrix
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<div style="margin: 12px 0px; font-family: arial; color: #333333; background: #ffffff; border: solid 4px #e5e5e5; width: 100%; clear: left;"><div class="CM_CTB_Content_Wrap" style="margin: 0px; padding: 0px;background-color: #ffffff;"><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content.clipmarks.com/blog_embed/bf8855e0-3cb6-4e56-a867-7e527d277883/27D6C00D-6AB9-4A19-8A5D-2E66C67933BE/" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://www.google.com.au/search?source=ig&hl=en&rlz=&=&q=inverse+matrices&btnG=Google+Search&meta=lr%3D" href="http://www.google.com.au/search?source=ig&hl=en&rlz=&=&q=inverse+matrices&btnG=Google+Search&meta=lr%3D" style="font-size: 11px;">www.google.com.au</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.google.com.au/search?source=ig&hl=en&rlz=&=&q=inverse+matrices&btnG=Google+Search&meta=lr%3D"><LI class="g"><H3 class="r"><A href="http://video.google.com.au/videosearch?source=ig&hl=en&rlz=&q=inverse+matrices&lr=&um=1&ie=UTF-8&ei=7wCuSufXC4_EsQO01PX5BA&sa=X&oi=video_result_group&ct=title&resnum=4">Video results for <EM>inverse matrices</EM></A></H3><TABLE class="ts"><TBODY><TR><TD width="280" valign="top" colspan="1"><DIV><TABLE class="ts"><TBODY><TR><TD valign="top"><A href="http://www.google.com.au/url?q=http://www.youtube.com/watch?v=iUQR0enP7RQ&ei=7wCuSufXC4_EsQO01PX5BA&sa=X&oi=video_result&resnum=4&ct=thumbnail&usg=AFQjCNEzb_MvAozCjLkFTV04eZtlbR60KA"><IMG width="80" height="60" border="1" alt="" src="http://img.youtube.com/vi/iUQR0enP7RQ/default.jpg?h=60&w=80&sigh=__04M7ApZYScq2FeF3cJ_bUdY8xyg=" /><DIV><IMG width="20" height="20" border="0" alt="" src="http://www.google.com.au/images/icons/sectionized_ui/play_c.gif" /></DIV></A></TD><TD valign="top"><A class="l" href="http://www.youtube.com/watch?v=iUQR0enP7RQ"><EM>Inverse Matrix</EM> (part 1)</A><BR /><FONT color="#666666">14 min</FONT><BR /><CITE>www.youtube.com</CITE></TD></TR></TBODY></TABLE></DIV></TD><TD width="280" valign="top" colspan="1"><DIV><TABLE class="ts"><TBODY><TR><TD valign="top"><A href="http://www.google.com.au/url?q=http://video.google.com/videoplay?docid=6785461979028631588&ei=7wCuSufXC4_EsQO01PX5BA&sa=X&oi=video_result&resnum=5&ct=thumbnail&usg=AFQjCNFbnb8qVXgGqhjf3AEI-j4HM3SVmQ"><IMG width="80" height="60" border="1" alt="" src="http://video.google.com/ThumbnailServer2?app=smh&contentid=615194f9571e398d&offsetms=2350000&itag=w160&sigh=MJeTxcEhkTiC77o2g1l10oXukQs&h=60&w=80&sigh=__iyAk3t_F3-o2jjc_sw0OHrgBLWo=" /><DIV><IMG width="20" height="20" border="0" alt="" src="http://www.google.com.au/images/icons/sectionized_ui/play_c.gif" /></DIV></A></TD><TD valign="top"><A class="l" href="http://video.google.com/videoplay?docid=6785461979028631588">MIT Math Lecture: Linear Algebra - 03 <B>...</B></A><BR /><FONT color="#666666">50 min</FONT><BR /><CITE>video.google.com</CITE></TD></TR></TBODY></TABLE></DIV></TD></TR><TR><TD width="280" valign="top" colspan="1"><DIV><TABLE class="ts"><TBODY><TR><TD valign="top"><A href="http://www.google.com.au/url?q=http://www.vimeo.com/clip:71218&ei=7wCuSufXC4_EsQO01PX5BA&sa=X&oi=video_result&resnum=6&ct=thumbnail&usg=AFQjCNFDfq0q7zrEIW7wuPitTHc2sWFIiA"><IMG width="80" height="60" border="1" alt="" src="http://video.google.com/ThumbnailServer2?app=smh&contentid=cc2c348392302cf3&offsetms=65000&itag=w160&sigh=hcS0iPPO1xNsMU9fjDoqghriqVI&h=60&w=80&sigh=__pL5Wnwq_7r-MtXd3Cyh63_9yeKc=" /><DIV><IMG width="20" height="20" border="0" alt="" src="http://www.google.com.au/images/icons/sectionized_ui/play_c.gif" /></DIV></A></TD><TD valign="top"><A class="l" href="http://www.vimeo.com/clip:71218"><EM>Inverse Matrices</EM></A><BR /><FONT color="#666666">3 min 29 sec</FONT><BR /><CITE>www.vimeo.com</CITE></TD></TR></TBODY></TABLE></DIV></TD></TR></TBODY></TABLE></LI></blockquote><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content7.clipmarks.com/images/clip-icon.gif" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://mathworld.wolfram.com/MatrixInverse.html" href="http://mathworld.wolfram.com/MatrixInverse.html" style="font-size: 11px;">mathworld.wolfram.com</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://mathworld.wolfram.com/MatrixInverse.html"><P class="Text">
For a <IMG width="27" height="14" border="0" alt="2×2" class="inlineformula" src="http://mathworld.wolfram.com/images/equations/MatrixInverse/Inline8.gif" /> <A class="Hyperlink" href="http://mathworld.wolfram.com/Matrix.html">matrix</A>
</P></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://mathworld.wolfram.com/MatrixInverse.html"><table background="undefined" bgcolor=""><tr><TD align="left"><IMG width="68" height="36" border="0" alt=" A=[a b; c d], " class="numberedequation" src="http://mathworld.wolfram.com/images/equations/MatrixInverse/NumberedEquation2.gif" /></TD></tr></table></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://mathworld.wolfram.com/MatrixInverse.html"><P class="Text">
the matrix inverse is
</P></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://mathworld.wolfram.com/MatrixInverse.html"><TABLE width="100%" cellspacing="0" cellpadding="0" border="0" align="center"><TBODY><TR><TD width="1" align="right"><IMG width="21" height="17" border="0" alt="A^(-1)" class="displayformula" src="http://mathworld.wolfram.com/images/equations/MatrixInverse/Inline9.gif" /></TD><TD width="14" align="center"><IMG width="9" height="14" border="0" alt="=" class="displayformula" src="http://mathworld.wolfram.com/images/equations/MatrixInverse/Inline10.gif" /></TD><TD align="left"><IMG width="78" height="40" border="0" alt="1/(|A|)[d -b; -c a]" class="displayformula" src="http://mathworld.wolfram.com/images/equations/MatrixInverse/Inline11.gif" /></TD><TD width="10" align="right"><DIV class="eqnum" id="eqn3">
(3)
</DIV>
</TD></TR><TR><TD width="1" align="right"><IMG width="12" height="14" border="0" alt="" class="displayformula" src="http://mathworld.wolfram.com/images/equations/MatrixInverse/Inline12.gif" /></TD><TD width="14" align="center"><IMG width="9" height="14" border="0" alt="=" class="displayformula" src="http://mathworld.wolfram.com/images/equations/MatrixInverse/Inline13.gif" /></TD><TD align="left"><IMG width="115" height="40" border="0" alt="1/(ad-bc)[d -b; -c a]." class="displayformula" src="http://mathworld.wolfram.com/images/equations/MatrixInverse/Inline14.gif" /></TD><TD width="10" align="right"><DIV class="eqnum" id="eqn4">
(4)
</DIV>
</TD></TR></TBODY></TABLE></blockquote><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content6.clipmarks.com/images/clip-icon.gif" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://www.edhelper.com/Matrices15.htm" href="http://www.edhelper.com/Matrices15.htm" style="font-size: 11px;">www.edhelper.com</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.edhelper.com/Matrices15.htm"><TABLE width="100%" border="0"><TBODY><TR valign="top"><TD width="3%">1.  </TD><TD>Find the inverse of:<BR /><TABLE cellspacing="0" cellpadding="0" border="0"><TBODY><TR><TD><IMG src="http://www.edhelperclipart.com/clipart/matlb2.jpg" /></TD><TD><TABLE cellspacing="0" cellpadding="0" border="0"><TBODY><TR><TD align="center">  1  </TD><TD align="center">  10  </TD></TR><TR><TD align="center">  -2  </TD><TD align="center">  -9  </TD></TR></TBODY></TABLE></TD><TD><IMG src="http://www.edhelperclipart.com/clipart/matrb2.jpg" /></TD></TR></TBODY></TABLE><BR /></TD></TR></TBODY></TABLE></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.edhelper.com/Matrices15.htm"><table background="undefined" bgcolor=""><TR valign="top"><TD width="3%">4.  </TD><TD>Find the inverse of:<BR /><TABLE cellspacing="0" cellpadding="0" border="0"><TBODY><TR><TD><IMG src="http://www.edhelperclipart.com/clipart/matlb2.jpg" /></TD><TD><TABLE cellspacing="0" cellpadding="0" border="0"><TBODY><TR><TD align="center">  -3  </TD><TD align="center">  5  </TD></TR><TR><TD align="center">  -10  </TD><TD align="center">  7  </TD></TR></TBODY></TABLE></TD><TD><IMG src="http://www.edhelperclipart.com/clipart/matrb2.jpg" /></TD></TR></TBODY></TABLE><BR /></TD></TR></table></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.edhelper.com/Matrices15.htm"><table background="undefined" bgcolor=""><TR valign="top"><TD width="3%">8.  </TD><TD>Find the inverse of:<BR /><TABLE cellspacing="0" cellpadding="0" border="0"><TBODY><TR><TD><IMG src="http://www.edhelperclipart.com/clipart/matlb2.jpg" /></TD><TD><TABLE cellspacing="0" cellpadding="0" border="0"><TBODY><TR><TD align="center">  -6  </TD><TD align="center">  -2  </TD></TR><TR><TD align="center">  -4  </TD><TD align="center">  8  </TD></TR></TBODY></TABLE></TD><TD><IMG src="http://www.edhelperclipart.com/clipart/matrb2.jpg" /></TD></TR></TBODY></TABLE><BR /></TD></TR></table></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.edhelper.com/Matrices15.htm"><table background="undefined" bgcolor=""><TR valign="top"><TD width="3%">11.  </TD><TD>Find the inverse of:<BR /><TABLE cellspacing="0" cellpadding="0" border="0"><TBODY><TR><TD><IMG src="http://www.edhelperclipart.com/clipart/matlb2.jpg" /></TD><TD><TABLE cellspacing="0" cellpadding="0" border="0"><TBODY><TR><TD align="center">  9  </TD><TD align="center">  -1  </TD></TR><TR><TD align="center">  -12  </TD><TD align="center">  2  </TD></TR></TBODY></TABLE></TD><TD><IMG src="http://www.edhelperclipart.com/clipart/matrb2.jpg" /></TD></TR></TBODY></TABLE><BR /></TD></TR></table></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.edhelper.com/Matrices15.htm"><table background="undefined" bgcolor=""><TR valign="top"><TD width="3%">14.  </TD><TD>Find the inverse of:<BR /><TABLE cellspacing="0" cellpadding="0" border="0"><TBODY><TR><TD><IMG src="http://www.edhelperclipart.com/clipart/matlb2.jpg" /></TD><TD><TABLE cellspacing="0" cellpadding="0" border="0"><TBODY><TR><TD align="center">  -4  </TD><TD align="center">  7  </TD></TR><TR><TD align="center">  5  </TD><TD align="center">  -2  </TD></TR></TBODY></TABLE></TD><TD><IMG src="http://www.edhelperclipart.com/clipart/matrb2.jpg" /></TD></TR></TBODY></TABLE><BR /></TD></TR></table></blockquote></div><div style="margin: 0px 6px 6px 4px;"><table style="font-size: 11px;border-spacing: 0px;padding: 0px;" cellpadding="0" cellspacing="0" width="100%"><tr><td style="background:transparent;border-width:0px;padding:0px;">&nbsp;</td><td align="right" style="background:transparent;border-width:0px;padding:0px;width:107px" width="107"><a href="http://clipmarks.com/share/27D6C00D-6AB9-4A19-8A5D-2E66C67933BE/blog/" title="blog or email this clip"><img src="http://content7.clipmarks.com/images/c2b-foot.png" border="0" alt="blog it" width="107" height="17" style="border-width:0px;padding:0px;margin:0px;" /></a></td></tr></table></div></div>
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