Q$.6(HW$#$10)$

$(1)$ The following vector represents the distribution of final scores in a course:

$G=[68,83,61,70,75,82,57,5,76,85,62,71,96,78,76,68,72,75,83,93]$

Write a MATLAB code to determine how many times the final scores are below $75$ :

$($a$)$ Using for loop.

$($b$)$ Using while loop.

$(2)$ A list of $30$ exam scores is: $31,70,92,5,47,88,81,73,51,76,80,90,55,23,43,98,36,87,22,61,19,69,26,82,89,99,71,59,49,36.$

Write a MATLAB program that determines how many grades are between $0$ and $19,$ between $20$ and $39,$ between $40$ and $59,$ between $60$ and $79,$ and between $80$ and $100.$

In the program while loop and if statement should be used. The results should be displayed in a table form showing the number of grades in each range.

$0\mathrm{.}7(HW$#$10)$

$(1)$ The following array $P$ represents the prices, in $$,$ of different goods in a store:

$P=[12,7\mathrm{.}95,88,26\mathrm{.}5,27\mathrm{.}9,3\mathrm{.}5,57,65\mathrm{.}9,17\mathrm{.}7,35\mathrm{.}6,15,96\mathrm{.}5]$

A discount strategy is applied as follow:

$10\%$ discount for goods that are less than $10$$

$15\%$ discount for goods that are between $10$$ and $30$$

$20\%$ discount for goods that are above $30$$

Write a MATLAB program to define the prices $P$ and returns an array representing the prices after application of the discount. You must use for loop and if statement to find the new prices. Display your results in a table with headings showing the prices before and after discount.

$(2)$ Pascal lower$-$triangular matrix $(L)$ consists of $(m)-$rows and $(n)-$columns can be represented as follows:

$L_{mxn}=([1,0,0,0,0,$dots$],[1,1,0,0,0,$dots$],[1,2,1,0,0,$dots$],[1,3,3,1,0,$dots$],[1,4,6,4,1,$dots$],[dots,$dots,dots,dots,dots,dots$])$

Based on the above representation for any row $(i)$ and column $(j),$ the following conditions are true:

The first column and the diagonal positions take the value of $1.$

The upper triangle contains zeros.

The rest of the elements is the sum of the two values in the row above it$.$

Write a MATLAB program to create an $($mxn$)$ Pascal lower$-$triangular matrix $($L$)$ according to the following steps:

$($a$)$ The program first prompts the user to enter the size of the matrix $($enter the number of rows $(m)$ and the number of the columns $(n)).$

$($b$)$ The program calls a MATLAB function named "LowTri"$-$with $2$ inputs and $1$ output$-$ and uses a nested$-$for$-$loop and branching$-$if$-$statement to create $L_{m.xn}.$

$($c$)$ Execute the program for the case of $L_{7x}7$ and display the matrix.

$($d$)$ Use the matrix obtained to get and then display the Pascal upper$-$triangular matrix $(U_{7x7})$ and the Pascal symmetric matrix $(S_7).$