mathmari
Gold Member
MHB
- 4,984
- 7
Hey! 
Let $\mathbb{K}$ be a fiels and $A\in \mathbb{K}^{p\times q}$ and $B\in \mathbb{K}^{q\times r}$.
I want to show that $\text{Rank}(AB)\leq \text{Rank}(A)$ and $\text{Rank}(AB)\leq \text{Rank}(B)$.
We have that every column of $AB$ is a linear combination of the columns of $A$, or not? (Wondering)
What can we do to show the inequality? (Wondering)

Let $\mathbb{K}$ be a fiels and $A\in \mathbb{K}^{p\times q}$ and $B\in \mathbb{K}^{q\times r}$.
I want to show that $\text{Rank}(AB)\leq \text{Rank}(A)$ and $\text{Rank}(AB)\leq \text{Rank}(B)$.
We have that every column of $AB$ is a linear combination of the columns of $A$, or not? (Wondering)
What can we do to show the inequality? (Wondering)