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<b>let </b><font color="Maroon" title="c1">K</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/><b>let </b><font color="Maroon" title="c2">r</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Scalar</a> of <font color="Maroon" title="c1">K</font>;<br/><b>let </b><font color="Maroon" title="c3">V</font> be   <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">K</font>;<br/><b>let </b><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Vector</a> of <font color="Maroon" title="c3">V</font>;<br/><b>let </b><font color="Maroon" title="c6">W</font> be    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c3">V</font>;<br/>











<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="lmod_7.html#K18" title="LMOD_7:func.18">/</a> <font color="Maroon" title="c6">W</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lmod_7.html#K18" title="LMOD_7:func.18">/</a> <font color="Maroon" title="c6">W</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="lmod_7.html#K14" title="LMOD_7:func.14">.</a> <font color="Maroon" title="c6">W</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lmod_7.html#K14" title="LMOD_7:func.14">.</a> <font color="Maroon" title="c6">W</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="lmod_7.html#K18" title="LMOD_7:func.18">/</a> <font color="Maroon" title="c6">W</font>
<b>by </b><i><a class="ref" href="lmod_7.html#T24" target="_self" title="LMOD_7:th.24">Th24</a></i>
;<br/>

<b>thus </b><font color="Maroon" title="c2">r</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="lmod_7.html#K18" title="LMOD_7:func.18">/</a> <font color="Maroon" title="c6">W</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="lmod_7.html#K16" title="LMOD_7:func.16">LMULT</a> <font color="Maroon" title="c6">W</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c2">r</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="lmod_7.html#K14" title="LMOD_7:func.14">.</a> <font color="Maroon" title="c6">W</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D24" title="VECTSP_1:def.24">VECTSP_1:def 24</a></i>
<br/>.= 
<font color="Maroon" title="c2">r</font> <a href="lmod_7.html#K15" title="LMOD_7:func.15">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="lmod_7.html#K14" title="LMOD_7:func.14">.</a> <font color="Maroon" title="c6">W</font></span>)</span>
<b>by </b><i><a class="ref" href="lmod_7.html#D21" target="_self" title="LMOD_7:def.21">Def21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="lmod_7.html#K18" title="LMOD_7:func.18">/</a> <font color="Maroon" title="c6">W</font>
<b>by </b><i><a class="ref" href="lmod_7.html#D20" target="_self" title="LMOD_7:def.20">Def20</a></i>
;<br/>


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