Question 1159894
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<pre>

Let  "p"  and  "q"  be two "free" parameters, i.e. arbitrary real numbers.


Consider the vectors  u = (-7p,2p,0)  and  v = (-2q,0,q).


They both belong to the given subspace in {{{R^3}}}.


    Indeed, for  "u" :   -2*(-7p) - 7*(2p) - 4*0 = 14p - 14p - 0 = 0;

    and     for  "v" :   -2*(-2q) - 7*0 - 4*q    =  4q -  0 - 4q = 0.



Also, it is OBVIOUS that these vectors are LINEARLY INDEPENDENT.


Therefore, they form the basis in the given 2D subspace.
</pre>

Solved.


"u" and "v" are the desired vectors.



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