Solution Found!
Prove Proposition 4.4. (Hint: Exercise 15 and Proposition 4.3 may be useful.) _
Chapter 3, Problem 16(choose chapter or problem)
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,
.