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Chapter 2: Q2.9-20E (page 93)

In Exercises 19-24, justify each answer or construction.

What is the rank of a \({\bf{4}} \times {\bf{5}}\) matrix whose null space in three dimensional.

Short Answer

Expert verified

The dimension of the null space of A is 2.

Step by step solution

01

Find the dimension of Nul A

There are five columns in the matrix, and the null space is three dimensional. So, the dimension of Nul A is 3.

02

Find the rank A

According to the rank theorem,

\(\begin{array}{c}{\rm{rank}}\;A = 5 - 3\\ = 2.\end{array}\)

So, the dimension of the null space of A is 2.

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