Matlab1

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Apr 3, 2024

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Exercise 1.1 What is the date of your MATLAB quiz? What day of the week is that? 0:00 am PT on Wednesday, June 7th until 11:59 pm PT on Thursday, June 8th. When is each homework due? What day of the week is that? 1. Introduction to MATLAB Due at 11:59pm on Friday, April 14 PT 2. Systems of Linear Equations Due at 11:59pm on Friday, April 28 PT 3. Matrix Algebra Due at 11:59pm on Friday, May 12 PT 4. Eigenvalues & Diagonalization Due at 11:59pm on Friday, May 26 PT 5. Orthogonality & Least Squares Due at 11:59pm on Friday, June 9 PT

Exercise 1.2 Define each letter of your first and last names to be the number corresponding to its place in the alphabet. Then set your name, without any spaces, equal to the sum of the letters. >> t=20;i=9;c=3;a=1;n=14;y=25;u=21;m=13;o=15; >> TianyuMiao=t+i+a+n+y+u+m+i+a+o TianyuMiao = 128

Exercise 1.3 Suppose we want to evaluate the expression Enter the command >> z = 25-(100-7exp(5+cos(pi/3)) You will get an error message. Use the up-arrow to bring this line back, and then use the left and right arrow keys to correct the error(s). Include the wrong command, the error message, and your fix in your homework. [Hint: Multiplication and parentheses are good things to check.] >> z = 25-(100-7*exp (5+cos(pi/3))) z = 1.6378e+03

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Exercise 1.4 Compute the derivative of log(cos(t)-3*s) with respect to t. Next, differentiate the same function with respect to s instead. Include the input and output in your Word document. >> syms s t >> diff(log(cos(t)-3*s),t) ans = sin(t)/(3*s - cos(t)) >> diff(log(cos(t)-3*s),s) ans = 3/(3*s - cos(t))

Exercise 1.5 Compute arcsin(1) using MATLAB. Include the outputs in MATLAB. [Hint: Start by looking at help sin, or perhaps doc arcsine.] >> asin(1) ans = 1.5708

Exercise 1.6 Input the following matrix into MATLAB Include your commands and outputs in MATLAB. >> Fibonacci= [1 1 2 3; 5 8 13 21; 34 55 89 144; 233 377 610 987] Fibonacci = 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987

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Exercise 1.7 Using the commands introduced above, construct a new matrix with whatever name you like from Fibonacci that consists of the elements in the last two rows and the middle two columns of Fibonacci. (The result should therefore be a 2×2 matrix.) Be sure to include the command you used and the resultant output in your Word document. >> Fibonacci(3:4,2:3) ans = 55 89 377 610

Exercise 1.8 Create two random 4×4 matrices named A and B. Do you expect A + B and B + A to be equal? Compute those two sums using MATLAB. Are they in fact the same? I thought they will be different (I thought it will generate each time they calculate) but in fact they are the same. >> A=rand(4) A = 0.6557 0.6787 0.6555 0.2769 0.0357 0.7577 0.1712 0.0462 0.8491 0.7431 0.7060 0.0971 0.9340 0.3922 0.0318 0.8235 >> B=rand(4) B = 0.6948 0.4387 0.1869 0.7094 0.3171 0.3816 0.4898 0.7547 0.9502 0.7655 0.4456 0.2760 0.0344 0.7952 0.6463 0.6797 >> A+B ans = 1.3506 1.1175 0.8424 0.9863 0.3528 1.1393 0.6610 0.8009 1.7994 1.5086 1.1516 0.3732 0.9684 1.1874 0.6781 1.5032 >> B+A ans = 1.3506 1.1175 0.8424 0.9863

0.3528 1.1393 0.6610 0.8009 1.7994 1.5086 1.1516 0.3732 0.9684 1.1874 0.6781 1.5032

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Matlab1

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