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Q10E

Expert-verified
Found in: Page 191

### Linear Algebra and its Applications

Book edition 5th
Author(s) David C. Lay, Steven R. Lay and Judi J. McDonald
Pages 483 pages
ISBN 978-03219822384

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# 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.

See the step by step solution

## Step 1: Find the rank of the matrix

Using the nullity theorem, you get:

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

## Step 2: Find the dimension of the column space

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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