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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th18</font></span>: <a NAME="T21"><span class="comment"><font color="firebrick">:: ANPROJ_8:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">r</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 3</span>)</span><br/>  for <font color="Olive" title="b4">M</font> being   <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of 3,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  st <font color="Olive" title="b4">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">r</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> holds <br/>( <font color="Olive" title="b4">M</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a>  &amp; <font color="Olive" title="b4">M</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,2) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a>  &amp; <font color="Olive" title="b4">M</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,3) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a>  &amp; <font color="Olive" title="b4">M</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (2,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a>  &amp; <font color="Olive" title="b4">M</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (2,2) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a>  &amp; <font color="Olive" title="b4">M</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (2,3) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a>  &amp; <font color="Olive" title="b4">M</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (3,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">r</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a>  &amp; <font color="Olive" title="b4">M</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (3,2) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">r</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a>  &amp; <font color="Olive" title="b4">M</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (3,3) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">r</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a>  )</div></div>
