MATLAB Questions. Part $3$ Exercises

Recall that $a=$ last digit of your student ID$,b=$ second to last digit of your student ID$,c=$ third to last digit of

your student ID$,$ and $d=$ the sum of the last three digits of your student ID$.$ Complete the following operations in

your script, making new lines for each operation.

$(a+1)x+(b+1)y=-9$

$(c+1)x+(d+1)y=-4$

$3$A$)($Solve system of linear equations, Method $1)$ Solve the above system of linear equations using reduced row

echelon form. In other words, declare a $23$ coefficient matrix called P$3$AM for the system above $($make a matrix

with just numbers, no variables$),$ then use the reduced row echelon form command to solve the system. Declare

the solution in MATLAB as P$3$A$\mathrm{.}3$B$)($Solve system of linear equations, Method $2)$ Solve the same system of linear equations using an inverse

matrix. In other words, declare a $22$ coefficient matrix called P$3$BM for the same system $($make a matrix with

just numbers, no variables, but only for the side with the $x$ and $y$ on it$),$ then declare a $21$ vector called P$3$BV

with the numbers on the right side of the equation. If we let $x=[x$;$y],$ then the system turns into $(P3BM)(x)=$

$($P$3$BV$)$; therefore, the solution to the system should be $x=(P3BM{)}^{-1}(P3BV).$ Use the proper inverse matrix

operation and declare the solution in MATLAB as P$3$B$.$ Check that your results match the prior method from $3$A$.$ The work should be done by using the MATLAB.