(Solved): MATLAB The standard equation of the hyperbola with center \( \left(a_{12}, a_{21}\right) \) is \[ z= ...

The standard equation of the hyperbola with center \( \left(a_{12}, a_{21}\right) \) is \[ z=f(x, y)=\frac{\left(x-a_{12}\right)^{2}}{a_{11}^{2}}-\frac{\left(y-a_{21}\right)^{2}}{a_{22}^{2}}=1 \] where \( a_{11}, a_{12}, a_{21}, a_{22} \) can be considered to be the elements of a \( 2 \times 2 \) matrix \( \left[a_{11} a_{12}\right. \); \( a_{21} a_{22} \) ]. Complete the following in a MATLAB script file. (a) Read a \( 2 \times 2 \) matrix from the user and store it in \( \mathbf{A} \). (b) Check if dimensions of \( \mathbf{A} \) (entered by user) are \( 2 \times 2 \). If not, display error message. (c) Check if \( a_{11} \) and \( a_{22} \) are not zero. If yes, display error message. (d) Create vectors \( \mathbf{x} \) and \( \mathbf{y} \) ranging from \( -2 \) to 2 with a spacing of \( 0.1 \). (e) Use mesh-grid to create matrices \( \mathbf{X} \) and \( \mathbf{Y} \). (f) Create the matrix \( \mathbf{Z} \) using \( \mathbf{X}, \mathbf{Y} \) and the equation described above. Use a userdefined function to do this. (g) Create a \( 2 \times 2 \) subplots of the following: mesh plot, surface plot, contour plot and combination (surface + contour) plot of the function defined by \( \mathbf{Z} \). Add title and axis labels for each subplot.