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Linear Algebra - Four Fundamental Subspaces

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(The material is from the Four Fundamental Subspaces. Please show each step of your solution. )

Theorem 4.7:

Let A be an m x n matrix. Then

1. R (A) ┴ = N (A)
2. N (A) ┴ = R (A)
3. C (A) ┴ = N (A┬)
4. N (A┬) ┴ = C (A)

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This solution is comprised of a detailed explanation to answer Linear Algebra - Four Fundamental Subspaces.

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Proof:
(a) For any , we have , then .
On the other hand, if , then .
We note that is actually a linear ...

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