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 ?

• A. Rowspace(A) ⊆ Rowspace(B)
• B. Rowspace(A) ⊆ Rowspace(C)
• C. Colspace(A) ⊆ Colspace(B)
• D. Colspace(A) ⊆ Colspace(C)

Answer 1

Answer: (B), (C)

Rowspace(A) ⊆ Rowspace(C)

Answer 2

The correct option is (B) : Rowspace(A) ⊆ Rowspace(B) and (C) : Colspace(A) ⊆ Colspace(B).