document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1058626>Question 1058626</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let<BR>\n" );
document.write( "B =\r<BR>\n" );
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document.write( "1    0  0<BR>\n" );
document.write( "b21  1  0<BR>\n" );
document.write( "b31 b32 1<BR>\n" );
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document.write( "Find B^2.<BR>\n" );
document.write( "Find specific values of b21;b31;b32, such that B^2 = I3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #673719 by </B><A HREF=/tutors/aboutme.mpl?userid=solve_for_x><B>solve_for_x(190)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solve_for_x><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=673719\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The matrix B^2 is:\r<BR>\n" );
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document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=solve_for_x&illustration_name=Matrices.png\">\r<BR>\n" );
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document.write( "To make B^2 = I3, the following must be true:\r<BR>\n" );
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document.write( "2b21 = 0 --> b21 = 0\r<BR>\n" );
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document.write( "2b32 = 0 --> b32 = 0\r<BR>\n" );
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document.write( "2b31 + b21b32 = 0 --> 2b31 + 0*0 = 0 --> b31 = 0\r<BR>\n" );
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document.write( "Thus, b21, b31, and b32 must all be 0.\r<BR>\n" );
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document.write( "Edit in response to follow-up comment from OP:\r<BR>\n" );
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document.write( "If b22 = -1 instead of b22 = 1 as originally posted, then B^2 would be:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=solve_for_x&illustration_name=Matrices2.png\">\r<BR>\n" );
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document.write( "In this case, b21 and b32 could be any value to make B^2 = I3. In addition,<BR>\n" );
document.write( "b31 = -(b21 * b32)/2. </SPAN>\n" );
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