Question:
For a matrix M, let Rowspace(M) denote the linear span of the rows of M and Colspace(M) denote the linear span of the columns of M. Which of the following hold(s) for all A, B, C ∈ M10(\(\R\)) satisfying A = BC ?
For a matrix M, let Rowspace(M) denote the linear span of the rows of M and Colspace(M) denote the linear span of the columns of M. Which of the following hold(s) for all A, B, C ∈ M10(\(\R\)) satisfying A = BC ?
Updated On: Aug 13, 2024
- Rowspace(A) ⊆ Rowspace(B)
- Rowspace(A) ⊆ Rowspace(C)
- Colspace(A) ⊆ Colspace(B)
- Colspace(A) ⊆ Colspace(C)
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The Correct Option is B, C
Solution and Explanation
The correct option is (B) : Rowspace(A) ⊆ Rowspace(B) and (C) : Colspace(A) ⊆ Colspace(B).
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