# Linear Algebra - Four Fundamental Subspaces

Not what you're looking for? Search our solutions OR ask your own Custom question.

(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) â”´ = N (A)

2. N (A) â”´ = R (A)

3. C (A) â”´ = N (Aâ”¬)

4. N (Aâ”¬) â”´ = C (A)

https://brainmass.com/math/linear-algebra/linear-algebra-four-fundamental-subspaces-175054

#### Solution Preview

Please see the attachment.

Proof:

(a) For any , we have , then .

On the other hand, if , then .

We note that is actually a linear ...

#### Solution Summary

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

$2.49