Space of all matrices with given column space
Let $V$ be the vector space of all $m \times n$ (assume $m \leq n$) matrices $M$ over a field $\mathbb{F}$ whose column space satisfies $\operatorname{colsp}(M) \subseteq W$, where $W \subseteq \mathbb{F}^m$ is a given subspace. Prove that $\operatorname{dim}_\mathbb{F}(V) = n \operatorname{dim}_\mathbb{F}(W)$.
107
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
1 Attachment
1.6K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 510 views
- $10.00
Related Questions
- Consider the matrix, calculate a basis of the null space and column space
- The Span and Uniqueness of Solutions in a Parametric Matrix
- Linear Algebra Help : Consider Two Planes, P1 and P2
- Stuck on this and need the answer for this problem at 6. Thanks
- Linear algebra
- Linear Algebra Assistance: Linear Combinations of Vectors
- Linear Algebra Exam
- Determine values of some constant which equate linear operators whose linear transformation is through a different basis of the same vector space.