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write the solutions in the command window and then copy it to word. It should be an easy homework. Please be as fast as possible. Thank you.

Assignment Description



1.    (10 points) Consider the following matrices:


A =      3          2          8                                  B =      4          2          5          6

            -5         6          0                                              -3        0          7          1

                                                                                    8          -4         9          16


a.    Determine the sum and product of each matrix column using built-in MATLAB matrix functions

b.    Multiply each element of A by 3 and divide each element of B by 4.

c.    Multiply matrix A by matrix B.  Save your answer as a new matrix, C



2.    (15 points) In heat transfer, radiation emitted from a black body (an object that does not reflect any light) is measured by the Stefan-Boltzmann law:



Where E is the emittance (in W/m2), T is temperature (in Kelvin), and σ is the Stefan-Boltzmann constant, 5.67*10-8 W/(m2K4).  Write a function (.m file) that solves for the temperature of a black body that emits 6000 W/m2.  Round your answer to the nearest integer.


HINT: Use the nthroot function when solving for T.


3.    (20 points) Consider a generic chemical reaction, A à B + C, where a compound dissociates into two products.   The concentration, c, of component A is measured at 10-minute time (t) intervals, as shown in the table below:


t, min







c, ppm








The engineer analyzing the data creates the following model equation to approximate the concentration for any value of t:



It is common practice in science and engineering to plot discrete data points using symbols or markers, and to plot a mathematical model function using a continuous line. Therefore:


a.    Plot the data using magenta diamond-shaped markers

b.    Plot the model on the same graph using a solid green line

Be sure to include a legend, axis labels, axis limits, and an appropriate chart title.



4.    (25 points) The “butterfly curve” is a famous set of parametric equations, which are shown below:



a.    Create an array for t that ranges from 0 to 100 in intervals of 1/16 (or 0.0625)

b.    Generate x and y values using your t vector.  Note: You MUST use the element-by-element multiplication and exponentiation commands (.* & .^, respectively) rather than just the star (*) or carat (^)

c.    Plot x vs. t and y vs. t on the same figure.  Use a solid blue line x and a solid red line for y, along with a legend and appropriate chart & axis titles.

d.    Using the subplot command, stack your plot from part c on top of a plot of y vs. x.  Give this plot a title and axis labels as well. Can you see where the name “butterfly curve” comes from?!


5.    (25 points) The vapor pressure of a component as a function of temperature can be predicted from the Antoine Equation:




                                    A, B, and C are constants for a given component

                                    T is the Temperature in Kelvin

                                    P* is the Vapor Pressure in mm Hg


a.    Write a main program (.m file) in MATLAB that will calculate the vapor pressures of benzene between 300-600 Kelvin in increments of 30 K. The program should call a single function (separate .m file) called antoine, which will pass the Antoine constants and return (output) P* for each calculation of the vapor pressure.


The user should be prompted to enter a 1 or a 2 to select the type of loop used for the problem. Use a switch structure to solve the problem for either case - when case 1 is selected, a for loop should execute; when case 2 is selected, a while loop should run.  In both cases, store the values of the temperature and pressure in a matrix


b.    Use fprintf statements to print the your matrix as a table with the following headings:



                                    Temperature                Vapor Pressure            

                                    (deg. Celsius)                    (mm Hg)                    


Remember to convert from Kelvin to degrees Celsius. 


c.    Finally, plot the vapor pressures as a function of temperature on a single plot, which is labeled appropriately.  Use data markers of your choosing rather than a continuous curve.


                        Constants for Antoine Equation:


                                                                        A                                 B                     C

                        Benzene                                15.9008                      2788.1            -52.36





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