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<b>consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="vectsp_1.html#NM6">VectSp</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>take </b>
 <a href="vectsp_4.html#K1">(0).</a> <font color="Maroon">c<sub>2</sub></font>
;<br/>

<b>thus </b><a NAME="E2:17_1_1"/>
 <a href="vectsp_4.html#K1">(0).</a> <font color="Maroon">c<sub>2</sub></font> is <a href="vectsp_1.html#V11">strict</a>
 ;<br/>

<b>take </b><font color="Maroon">c<sub>3</sub></font> =  <a href="subset_1.html#K1">{}</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="vectsp_4.html#K1">(0).</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="matrlin.html#D3" target="_self">MATRLIN:def 3</a><br/>

<a NAME="E3:17_1_1"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="vectsp_7.html#V1">linearly-independent</a>
 
<b>by </b><i><a class="ref" href="vectsp_7.html#T4">VECTSP_7:4</a></i>;<br/>
<a NAME="E4:17_1_1"/>
 <a href="vectsp_7.html#K1">Lin</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="vectsp_4.html#K1">(0).</a> <span class="p1">(<span class="default"><a href="vectsp_4.html#K1">(0).</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="vectsp_7.html#T14">VECTSP_7:14</a></i>;<br/>
<a NAME="E5:17_1_1"/><b>then </b>
 <a href="vectsp_7.html#K1">Lin</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#G4">VectSpStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="vectsp_4.html#K1">(0).</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><a href="vectsp_4.html#K1">(0).</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,the <a href="struct_0.html#U2">Zero</a> of <span class="p1">(<span class="default"><a href="vectsp_4.html#K1">(0).</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,the <a href="vectsp_1.html#U2">lmult</a> of <span class="p1">(<span class="default"><a href="vectsp_4.html#K1">(0).</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="vectsp_4.html#T47">VECTSP_4:47</a></i>;<br/>
<b>hence </b><a NAME="E6:17_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is    <a href="vectsp_7.html#M1">Basis</a> of  <a href="vectsp_4.html#K1">(0).</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="matrlin.html#E3:17_1_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="vectsp_7.html#D3">VECTSP_7:def 3</a></i>;<br/>


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