document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1006564>Question 1006564</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A square matrix A is called symmetric if A^t = A. If B is a square matrix, then B.B^t and B + B^t are symmetric<BR>\n" );
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document.write( " is this statement true or false and why?  \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 #622682 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=622682\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First part of the statement\r<BR>\n" );
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document.write( "Given:<BR>\n" );
document.write( "B is square\r<BR>\n" );
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document.write( "since B is square, this means B*B^T is defined\r<BR>\n" );
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document.write( "we want to prove<BR>\n" );
document.write( "(B*B^T)^T = B*B^T<BR>\n" );
document.write( "is true\r<BR>\n" );
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document.write( "(B*B^T)^T = B*B^T<BR>\n" );
document.write( "(B^T)^T*B^T = B*B^T ... use <a  rel=nofollow HREF= \"https://en.wikipedia.org/wiki/Transpose\">property 3</a><BR>\n" );
document.write( "B*B^T = B*B^T ...  ... use <a  rel=nofollow HREF= \"https://en.wikipedia.org/wiki/Transpose\">property 1</a>; we end up with a true equation\r<BR>\n" );
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document.write( "So the first part of the statement is true.\r<BR>\n" );
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document.write( "Now onto the second part of the statement\r<BR>\n" );
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document.write( "B is square ----> B+B^T is defined\r<BR>\n" );
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document.write( "we want to prove B+B^T is symmetric, so we want to show that <BR>\n" );
document.write( "(B+B^T)^T = B+B^T<BR>\n" );
document.write( "is true\r<BR>\n" );
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document.write( "(B+B^T)^T = B+B^T<BR>\n" );
document.write( "B^T+(B^T)^T = B+B^T ... use <a  rel=nofollow HREF= \"https://en.wikipedia.org/wiki/Transpose\">property 2</a><BR>\n" );
document.write( "B^T+B = B+B^T  ... use <a  rel=nofollow HREF= \"https://en.wikipedia.org/wiki/Transpose\">property 1</a><BR>\n" );
document.write( "B+B^T = B+B^T ... commutative property of matrix addition; true equation\r<BR>\n" );
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document.write( "The last true equation shows that (B+B^T)^T = B+B^T is true as well. So the second part of the statement is true.\r<BR>\n" );
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document.write( "Both parts of the statement have been proven true. Overall, the statement is true. </SPAN>\n" );
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