How can I show image of \lambda is equal to kernel $\displaystyle \mu$?

$\displaystyle 0\rightarrow {\frak m} \cap {\frak a} \stackrel{\lambda}{\rightarrow} {\frak m} \oplus {\frak a} \stackrel{\mu}{\rightarrow} {\frak m} + {\frak a} \rightarrow 0,$

where

$\displaystyle \lambda $ is defined as $\displaystyle x \mapsto (x,x)$ and $\displaystyle \mu$ is given by $\displaystyle (x,ya)\mapsto (x-ya).$