This question is on representing linear maps via matrix multiplication. For each linear map

R

m $$ R

n

: $(1)$ find the associated matrix with respect to the standard bases on the domain

and range; $(2)$ show your work verifying that your matrix does correspond to that linear map.

For a related example and result, see Class $16$ and Class $17$ notes.

$($a$).$ J

$$

$$

$$

$$

x

y

z

$$

$$

$$

$=$

$2$y $+$ z

$3$x $$ y

$($b$).$ K

x

y

$=$

$$

$$

y

x $$ y

$2$x $+$ y

$$

$($c$).$ L

$$

$$

$$

$$

x

y

z

$$

$$

$$

$=2$y $3$z