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<b>consider </b><font color="Maroon" title="c1">V</font> being   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>;<br/>
<b>take </b>
 <a href="rlsub_1.html#K1" title="RLSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font>
;<br/>

<b>thus </b><a NAME="E2:25_1_1"/>
 <a href="rlsub_1.html#K1" title="RLSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font> is <a href="rlvect_1.html#V1" title="RLVECT_1:attr.1">strict</a>
 ;<br/>

<b>take </b><font color="Maroon" title="c2">A</font> =  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="rlsub_1.html#K1" title="RLSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="rlvect_5.html#D1" target="_self" title="RLVECT_5:def.1">RLVECT_5:def 1</a><br/>

<a NAME="E3:25_1_1"/><i><font color="Green" title="E25">A1</font></i>: 
<font color="Maroon" title="c2">A</font> is <a href="rlvect_3.html#V1" title="RLVECT_3:attr.1">linearly-independent</a>
 
<b>by </b><i><a class="ref" href="rlvect_3.html#T8" title="RLVECT_3:th.8">RLVECT_3:8</a></i>;<br/>
<a NAME="E4:25_1_1"/>
 <a href="rlvect_3.html#K1" title="RLVECT_3:func.1">Lin</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlsub_1.html#K1" title="RLSUB_1:func.1">(0).</a> <span class="p1">(<span class="default"><a href="rlsub_1.html#K1" title="RLSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rlvect_3.html#T19" title="RLVECT_3:th.19">RLVECT_3:19</a></i>;<br/>
<a NAME="E5:25_1_1"/><b>then </b>
 <a href="rlvect_3.html#K1" title="RLVECT_3:func.1">Lin</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#G1" title="RLVECT_1:aggr.1">RLSStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="rlsub_1.html#K1" title="RLSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font></span>)</span>,the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">U2</a> of <span class="p1">(<span class="default"><a href="rlsub_1.html#K1" title="RLSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font></span>)</span>,the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">U4</a> of <span class="p1">(<span class="default"><a href="rlsub_1.html#K1" title="RLSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font></span>)</span>,the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <span class="p1">(<span class="default"><a href="rlsub_1.html#K1" title="RLSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="rlsub_1.html#T48" title="RLSUB_1:th.48">RLSUB_1:48</a></i>;<br/>
<b>hence </b><a NAME="E6:25_1_1"/>
<font color="Maroon" title="c2">A</font> is    <a href="rlvect_3.html#M1" title="RLVECT_3:mode.1">Basis</a> of  <a href="rlsub_1.html#K1" title="RLSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="txt" href="rlvect_5.html#E3:25_1_1"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="rlvect_3.html#D3" title="RLVECT_3:def.3">RLVECT_3:def 3</a></i>;<br/>


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