In Exercises 31–36, respond as comprehensively as

Chapter 2, Problem 31E

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QUESTION:

In Exercises 31–36, respond as comprehensively as possible, and justify your answer.

Suppose F is a \(5 \times 5\) matrix whose column space is not equal to \(\mathbb{R}^{5}\). What can you say about Nul F?

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QUESTION:

In Exercises 31–36, respond as comprehensively as possible, and justify your answer.

Suppose F is a \(5 \times 5\) matrix whose column space is not equal to \(\mathbb{R}^{5}\). What can you say about Nul F?

ANSWER:

Solution:-

Step1

Given that

Suppose F is a 5 × 5 matrix whose column space is not equal to .

Step2

To find

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