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.

$3$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$.$

$3$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 $3A.$

$3$C$)($Dot Product $-$ MAT $264)$ Declare P$3$C$1$ as a $12$ row vector with $a+1$

and $b+1$ as the two entries. Declare $PC_2$ as another $12$ row vector with

$c+1$ and $d+1$ as the two entries. Compute the dot product of these vectors

by multiplying the two vectors together, but transpose $PC_2$ before they are

multiplied. Declare your product in MATLAB as P$3$C$.$

$3$D$)($Eigenvalues $-$ MAT $364,$ Method $1)$ You are to solve for the

eigenvalues of a $22$ system of differential equations, given as

where $x=[x$;$y].$ Declare the coefficient matrix above P$3$DM in

MATLAB. You are going to find the eigenvalues of this matrix by

appropriately mimicking the lines of code below in MATLAB, but by using

relevant information and following proper syntax rules. Note that syms

allows you to define a variable in MATLAB symbolically. This command

will be used regularly in future projects.

syms Z

$==0,z$

$3$E$)($Eigenvalues $-$ MAT $364,$ Method $2)$ You are to find the eigenvalues of

the same $22$ system of differential equations as written above. Declare the

coefficient matrix as P$3$EM in MATLAB. You will use the eigenvalue

command from the list on the previous page to identify the eigenvalues of

this system. Declare your result in MATLAB as P$3$E$.$ Check that your

results match the prior method from $3$D$.$