$(10$ pts$)$ Task $11$: Consider the following multi$-$variable vector$-$valued function,

$f(x)=\left[\begin{array}{c}{x}_1^2+x_1{x}_2+x_2^2-3x_1+5\\ sin(x_1)+cos(x_2)\\ 1+3x_1-5x_2+2x_1{x}_2\end{array}\right]$

where $x=\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]$ is a vector of size $21.$

a$)$ What is the expression of Jacobian matrix?

b$)$ What is the expression of its linear approximation to $f(x+h)?$