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<b>let </b><font color="Maroon" title="c1">A</font> be   <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>

<b>reconsider </b><font color="Maroon" title="c2">e3</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> </span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> </span>)</span> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  ;<br/>
<a NAME="E2:38"/><i><font color="Green" title="E14">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span> )
 
;<br/>
<b>reconsider </b><font color="Maroon" title="c3">rr</font> = 1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  ;<br/>
3 <a href="matrixr1.html#K7" title="MATRIXR1:func.7">*</a> <font color="Maroon" title="c1">A</font> = 
 <a href="matrixr1.html#K2" title="MATRIXR1:func.2">MXF2MXR</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">e3</font> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p2">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrixr1.html#D7" target="_self" title="MATRIXR1:def.7">Def7</a></i>
<br/>.= 
 <a href="matrixr1.html#K2" title="MATRIXR1:func.2">MXF2MXR</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> </span>)</span> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> </span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> </span>)</span></span>)</span> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#T13" title="MATRIX_5:th.13">MATRIX_5:13</a></i>
<br/>.= 
 <a href="matrixr1.html#K2" title="MATRIXR1:func.2">MXF2MXR</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> </span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> </span>)</span></span>)</span> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#T10" title="MATRIX_5:th.10">MATRIX_5:10</a></i>
<br/>.= 
 <a href="matrixr1.html#K2" title="MATRIXR1:func.2">MXF2MXR</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> </span>)</span> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p4">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> </span>)</span> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p4">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#T13" title="MATRIX_5:th.13">MATRIX_5:13</a></i>
<br/>.= 
 <a href="matrixr1.html#K2" title="MATRIXR1:func.2">MXF2MXR</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> </span>)</span> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p4">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#T10" title="MATRIX_5:th.10">MATRIX_5:10</a></i>
<br/>.= 
 <a href="matrixr1.html#K2" title="MATRIXR1:func.2">MXF2MXR</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#T10" title="MATRIX_5:th.10">MATRIX_5:10</a></i>
<br/>.= 
 <a href="matrixr1.html#K2" title="MATRIXR1:func.2">MXF2MXR</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_3.html#T5" title="MATRIX_3:th.5">MATRIX_3:5</a>, <a class="txt" href="matrixr1.html#E2:38"><i><font color="Green" title="E14">A1</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E5:38"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrixr1.html#K3" title="MATRIXR1:func.3">+</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="matrixr1.html#K3" title="MATRIXR1:func.3">+</a> <font color="Maroon" title="c1">A</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> 3 <a href="matrixr1.html#K7" title="MATRIXR1:func.7">*</a> <font color="Maroon" title="c1">A</font>
 ;<br/>


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