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Q10E

Expert-verifiedFound in: Page 191

Book edition
5th

Author(s)
David C. Lay, Steven R. Lay and Judi J. McDonald

Pages
483 pages

ISBN
978-03219822384

**If the null space of A \({\bf{7}} \times {\bf{6}}\) matrix A is 4-dimensional, what is the dimension of the column space of A?**

The dimension of the column space of *A* is 1.

Using the **nullity theorem, you get**:

\(\begin{aligned} {\rm{rank}}\,A &= n - \dim \,{\rm{Nul}}\,A\\ &= 6 - 5\\ &= 1\end{aligned}\)

The dimension of the **column space** of *A* is equal to its rank.

So, the dimension of the column space of *A* is 1.

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