Show that a 5 x 7 matrix A must have 2$\leq$ nullity(A) $\leq$ 7.
Give an example of a 5 x 7 matrix A with nullity(A) = 2 and an example of a 5 x 7 matrix A with nullity(A) = 7.
2026-03-28 10:29:46.1774693786
Why a 5 x 7 matrix A must have 2 $\leq$ nullity(A) $\leq$ 7?
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Rank + Nullity = 7. Since the Rank can be as small as $0$, (e.g. the zero matrix) and as large as $5$ e.g. $$\begin{pmatrix}I&0 \\\end{pmatrix}$$ the nullity lies between $2$ and $7$.