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Let $A=\left[\begin{array}{cccc} 6 &-8 &-7 &1\cr -2 &6 &4 &-2\cr 2 &-6 &-4 &2\cr 2 &-6 &-4 &2 \end{array}\right].$
Find a basis for the null space of $A$ .

$\Bigg\lbrace$ $\left[\Rule{0pt}{4.8em}{0pt}\right.$ $\left]\Rule{0pt}{4.8em}{0pt}\right.$ , $\left[\Rule{0pt}{4.8em}{0pt}\right.$ $\left]\Rule{0pt}{4.8em}{0pt}\right.$ $\Bigg\rbrace.$