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<b>let </b><font color="Maroon" title="c1">A</font> be   <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of 3, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>

<b>reconsider </b><font color="Maroon" title="c2">N</font> =  <a href="matrixr2.html#K2" title="MATRIXR2:func.2">MXR2MXF</a> <font color="Maroon" title="c1">A</font> as   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of 3,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c3">N2</font> = <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,1</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,3</span>)</span></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>,<span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,1</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,3</span>)</span></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>,<span class="p2"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 3,1</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 3,2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 3,3</span>)</span></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> as   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of 3,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  <b>by </b><i><a class="ref" href="matrixr2.html#T35" target="_self" title="MATRIXR2:th.35">Th35</a></i>;<br/>
 <a href="matrixr2.html#K3" title="MATRIXR2:func.3">Det</a> <font color="Maroon" title="c1">A</font> = 
 <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Maroon" title="c3">N2</font>
<b>by </b><i><a class="ref" href="matrixr2.html#T37" target="_self" title="MATRIXR2:th.37">Th37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,1</span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,2</span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 3,3</span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,3</span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,2</span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 3,1</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,1</span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,3</span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 3,2</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,2</span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,3</span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 3,1</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,2</span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,1</span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 3,3</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,3</span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,1</span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 3,2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_9.html#T46" title="MATRIX_9:th.46">MATRIX_9:46</a></i>
;<br/>
<b>hence </b><a NAME="E4:42"/>
 <a href="matrixr2.html#K3" title="MATRIXR2:func.3">Det</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,2</span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 3,3</span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,3</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,2</span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 3,1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 3,2</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 3,1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,1</span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 3,3</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,3</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,1</span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 3,2</span>)</span></span>)</span>
 ;<br/>


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