Nutrition b$)$ Write MATLAB statements to define the necessary arrays for this system of equations:

c$)$ Try to solve the system of equations above in MATLAB. What is the result? Calculate the

residual. Does the solution appear to be valid?

d$)$ Use the rank function to demonstrate that the system is overdetermined $($i$.$e$.,$ has no

solution$).$

e$)$ Use the rref function on the augmented matrix to corroborate that the system is

overdetermined $($show command and result$).$

f$)$ Use array indexing in MATLAB to change the values of certain elements in your arrays, as

follows: $1.$ Change the target amount of vitamin C for the meal from $2160$ to $3380$ units.

Change the measured vitamin A content of food $2$ from $1200$ to $1199$ units per ounce.

Show the necessary commands:

g$)$ Solve the new system of equations in MATLAB. What is the result? Calculate the residual.

Does the solution appear to be valid? Verify using the rref function on the augmented matrix.

A dietitian wishes to plan a meal around three foods. The meal should include $8800$ units of vitamin A$,2160$ units of vitamin C$,$ and $1020$ units of calcium. Based on laboratory measurements, the number of units of the vitamins and calcium in one ounce of each food is indicated in the table below:

Nutrient content of foods $($units of nutrient per ounce of food$)$

$\backslash$table$[[$Nutrient$,$Food $1,$Food $2,$Food $3],[$Vitamin A$,400,1200,800],[$Vitamin C$,110,570,340],[$Calcium$,90,30,60]]$

a$)$ Arrange this information into a system of equations that would be used to find the appropriate quantity $($in ounces$)$ of each food that is needed to meet the nutritional objectives for the meal.