document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133224>Question 133224</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have been busting my head over a matrices problem where I need to find a pattern between the original square matrix (4, 2, 2, 4) and its exponential values. \r<BR>\n" );
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document.write( "The matrix squared is (20, 16, 16, 20) or 2(10, 8, 8, 10). \r<BR>\n" );
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document.write( "The matrix cubed is (112, 104, 104, 112) or 2(56, 52, 52, 56).\r<BR>\n" );
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document.write( "The matrix to the power of 4 is (656, 640, 640, 656) or 2(328, 320, 320, 328).\r<BR>\n" );
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document.write( "The matrix to the power of 5 is (3904, 3872, 3872, 3904) or 2(1952, 1936, 1936, 1952).\r<BR>\n" );
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document.write( "The matrix to the power of 7 is (140032, 139904, 139904, 140032) or 2(70016, 69952, 69952, 70016).\r<BR>\n" );
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document.write( "So far, what I have figured out is that the difference between the different elements in the matrices is always 2^n. As well, taking the original matrix, one can see that when k=3, the data inside the matrix is k+1 in two positions and k-1 in the other two. I can also factor out a 4 from each matrix, but that didn't seem to lead anywhere. \r<BR>\n" );
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document.write( "Can anyone help me with this emergency?\r<BR>\n" );
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document.write( "*Note: this question did not come from any textbook. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97461 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=97461\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I don't claim to know much about matix algebra. But I do see a pattern.\r<BR>\n" );
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document.write( "To get the first of each successive row, take <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%2A+the+outside+number+of+the+preceding+row+and+add+2+%2A+the+inside+number ALIGN=MIDDLE  ALT=\"4+%2A+the+outside+number+of+the+preceding+row+and+add+2+%2A+the+inside+number\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "To get the second number in the successive row, take <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%2A+the+inside+number+of+the+preceding+row+and+add+2%2A+the+outside+number ALIGN=MIDDLE  ALT=\"4+%2A+the+inside+number+of+the+preceding+row+and+add+2%2A+the+outside+number\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Thus, given (4,2,2,4) to get the second row, <BR>\n" );
document.write( "(4*4)+(2*2), (2*4)+(4*2),  (2*4)+(4*2), (4*4)+(2*2)<BR>\n" );
document.write( "(20, 16, 16, 20)\r<BR>\n" );
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document.write( "To get the third row from the second row,<BR>\n" );
document.write( "(4*20)+(2*16), (4*16)+(2*20),  (4*16)+(2*20), (4*20)+(2*16)<BR>\n" );
document.write( "(112, 104, 104, 112)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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