Prove Proposition 4.4. (Hint: Exercise 15 and Proposition 4.3 may be useful.) _

Chapter 3, Problem 16

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QUESTION:

Prove Proposition 4.4. (Hint: Exercise 15 and Proposition 4.3 may be useful.) _

Questions & Answers

QUESTION:

Prove Proposition 4.4. (Hint: Exercise 15 and Proposition 4.3 may be useful.) _

ANSWER:

Step 1 of 2

It is given that,

 is a -dimensional subspace.

To prove that, any  vectors that span  must be linearly independent, and any  linearly independent vectors in  must span .

That is, to prove that  is a basis of .

It is known that,

For  and  is a basis, and if  are vectors such that,.  

Then,

.

Also,

Suppose  and are the subspaces of  with the property that .  And if

.

Then,

.

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