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<b>let </b><font color="Maroon">V</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">u</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">w</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/>







<a NAME="E1:34"/>
( 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="real_1.html#K1">-</a> 1 &amp;  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">v</font> &amp;  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">w</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font> )
 
<b>by </b><i><a class="ref" href="rlvect_1.html#T29">RLVECT_1:29</a></i>;<br/>
<b>hence </b><a NAME="E2:34"/>
( <span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">u</font>,<font color="Maroon">w</font>,<font color="Maroon">v</font></span><a href="domain_1.html#K8">}</a></span> is <a href="rlvect_3.html#V1">linearly-independent</a> &amp; <font color="Maroon">u</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">v</font> &amp; <font color="Maroon">u</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">w</font> &amp; <font color="Maroon">v</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">w</font> implies <span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">u</font>,<span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">w</font></span>)</span>,<span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">v</font></span>)</span></span><a href="domain_1.html#K8">}</a></span> is <a href="rlvect_3.html#V1">linearly-independent</a> )
 <b>by </b><i/>;<br/>


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