Part $1$ Exercises

$1$A$)$ Open a new script $($top left button in Home menu$)$ and type your name and student ID number as comments in the top two lines of the script, as designated below. Comments in MATLAB start with a percent sign, MATLAB won't read anything after them, and these will be displayed as green text.

$\%$ First Name Last Name

$\%$ Student ID Number

For the remainder of this project, 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 a new line for each operation.

$1$B$)$ P$1$B $=$

$1$C$)$ PIC $=$

$1$D$)$ P$1$D $=$

Once you have these operations written in proper MATLAB syntax, go to your Editor menu and click Run. If there are values in your Command Window for all operations without error messages, then your code has successfully run! If you have error messages, read them carefully and try to

resolve them, then click Run again.

Part $2$ 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 a new line for each operation.

$2$A$)$ Define the matrices M$1,$ M$2,$ M$3,$ and M$4$ in different lines in your script so that they output the following matrices below $($the semicolons are important; include them!$).$ You will be using these to answer the questions that follow them.

$2$B$)$ P$2$B $=81$M$2-4$M$2$

$2$C$)$ P$2$C $=-3$M$4+732$

$2$D$)$ P$2$D $=($SM$2$M$3)($M$13)\%$ matrix multiply in parentheses, elementwise

multiply between parentheses

$2$E$)$ P$2$E $=(6$M$4$M$3)/($M$33)\%$ matrix multiply in first parentheses,

elementwise otherwise

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.

$3)($Solve system of linear equations, Method $1)$ Solve the above system of linear equations using reduced row echelon form. In other words, declare a $2$x$3$ 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

$.$

$3$B$)($Solve system of linear equations, Method $2)$ Solve the same system of linear equations using an inverse matrix. In other words, declare a $2\backslash$times $2$ 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 $2$x$1$ vector called P$3$BV with the numbers on the right side of the

equation. If we let X $=[$r ; y$],$ then the system turns into $($P$3$BM$)($X$)=$

$($P$3$BV$)$; therefore, the solution to the system should be X $=($P$3$BM$)\text{'}($P$3$BV$).$ 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$.$

$3$C$)($Dot Product $-$ MAT $264)$ Declare P$3$C$1$ as a $1$x$2$ row vector with a$+1$ and b$+1$ as the two entries. Declare P$3$C$2$ as another $1$x$2$ 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 P$3$C$2$ 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 $2$x$2$ 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

$\_=$ solve$($ z$^2-($ trace $(\_\_\_))$z $+$det$(\_\_\_)==0,$Z$)$

$3$E$)($Eigenvalues $-$ MAT $364,$ Method $2)$ You are to find the eigenvalues of the same $2$x$2$ 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$.$Form any student name and an $8$ digit student id number for this project