$5\mathrm{.}19$ Given the following state$-$variable models, obtain the expressions for the matrices $A,B,C,$ and $D$ for the given inputs and outputs.

a$.$ The outputs are $x_1$ and $x_2$; the input is $u.$

$x_1^{}=-5x_1+3x_2$

$x_2^{}=x_1-4x_2+5u$

b$.$ The output is $x_1$; the inputs are $u_1$ and $u_2.$

$x_1^{}=-5x_1+3x_2+4u_1$

$x_2^{}=x_1-4x_2+5u_2$