Find bases for the column space, the row space, and the null space of matrix A. You should verify that the Rank-Nullity Theorem holds.
$A = \left[\begin{array}{ccc} 1 &-2 &4\cr 1 &2 &6\cr 3 &-14 &8 \end{array}\right]$

Basis for the column space of A = $\Bigg\lbrace$

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,

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$\Bigg\rbrace$

Basis for the row space of A = $\Bigg\lbrace$

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,

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$\Bigg\rbrace$

Basis for the null space of A = $\Bigg\lbrace$

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$\Bigg\rbrace$