Suppose that to build a $33$ matrix in which the first column contains the sine of the elements between $\frac{5}{4}$ and $2,$ the second

column contains the sine of the elements between $\frac{}{4}$ and $\frac{3}{4},$ the third column contains the sine of the elements between $\frac{}{4}$ and $\frac{}{2}.$

Two spacing are required between the elements. You are requested to find the determinant and the inverse of the aforementioned

matrix $($Hint: Use linspace $(a,b,n)$ to build three rows and transpose of a matrix to find the columns of the aforementioned matrix$)$

a$)$ Sketch the flow diagram

b$)$ Write the MATLAB Code on the answer sheet to construct this matrix, to find the determinant and the inverse of this matrix.

c$)$ Add explanation $($comment$)$ for each line of this MATLAB Code.

d$)$ Run the m$-$script and show the screenshots on your answer sheet by using the "print screen" button on the keyboard.

e$)$ Discuss what it can be said about the matrix in terms of its determinant and in terms of its inverse.

Let you consider the following linear equation system.

$-2x_1+5x_2+4x_3-3x_4=9$

$x_1-7x_2+2x_3+9x_4=7$

$4x_1+3x_2+8x_3-6x_4=0$

$-6x_1+15x_2+12x_3-9x_4=27$

You are requested to solve system if possible.

a$)$ Sketch the flow diagram

b$)$ Write the MATLAB Code on the answer sheet to solve this equation system by finding its determinant and its inverse.

c$)$ Add explanation $($comment$)$ for each line of this MATLAB Code.

d$)$ Run the m$-$script and show the screenshots using the "print screen" button on the keyboard.

e$)$ Discuss what it can be said about the matrix in terms of its determinant and in terms of its inverse.

The data were taken in an isothermal batch reactor where reactant $A$ is decomposed to product $B.$

Write $m-$script in MATLABQ to achieve the following issues by using the data given in the table.

a$)$ Fit $2^{nd}-$order, $3^{rd}-$order and $4^{th}-$order polynomials to the given data and plot the data and these polynomials

b$)$ Label the $x-$axis and $y-$axis in terms of the variables defined in the given as above.

c$)$ Insert a title

d$)$ Insert a legend indicating the data, the $2^{nd}-$order, $3$ rd $-$order and $4$ th$-$order polynomials.