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1. (1 pt) Write the augmented matrix of the system -55x +4x=-91 -1x +7y-10z=-48 3. (1 pt) On the augmented matrix A below perform all three 61x+45y = -4 row operations in the order given, ((a) followed by (b) followed by (c)) and then write the resulting augmented matrix. 1 6 A 4 2. pt) 4 6 For each system, determine whether it has a unique solution (in this case, find the solution), infinitely many solutions, or no (a)r2 - -4ri Fr2 solutions (b)r3 3ri Fr3 1. (c)r3 2r2 tr3 5x+10y=0 3x +ly=0 A. Unique solution: 15,y=4 B. No solutions C. Unique solution: 0,y=0 D. Unique solution: = -1,y=5 4. (1 pt) Solve the system using matrices (row operations) E. Infinitely many solutions F. None of the above -2x+y =3, 2. 4x+2y =-18. 2x +5y=-21 -Gx-15y= 64 How many solutions are there to this system? A. Unique solution: 64,y=-21 B. Unique solution: =0,y=0 A. None C. No solutions B Exactly 1 D. Infinitely many solutions C. Exactly 2 E. Unique solution: -21,y=64 D. Exactly 3 F. None of the above E. Infinitely many F. None of the above 3. 3x+10y=-75 I 3x +9y=-06 A. Unique solution: 0,y=0 B. No solutions C. Unique solution: -5,y=-9 If there is one solution, give its coordinates in the answer spaces D. Unique solution: -9,y=5 below. E. Infinitely many solutions If there are infinitely many solutions, enter x in the answer F. None of the above blank for and enter a formula for y in terms of in the answer 4. blank for -5x +5y=35 If there are no solutions, leave the answer blanks for and y -10r+10y=70 empty. A. Infinitely many solutions B. Unique solution: 0, y=0 x = C. Unique solutionix 3, y=0 D. No solutions y E. Unique solution: 35, y 70 5. pt) Solve the system using matrices (row operations) If there is one solution, give its coordinates in the answer spaces below. -Grt5y+5z=52 If there are infinitely many solutions, enter in the answer x+2y+2==14 -++y+4x=25 blank for z enter a formula for y in terms of z in the answer blank for y and enter a formula for in terms of 2 in the answer How many solutions are there to this system? blank for A. None If there are no solutions, leave the answer blanks for x, and B. Exactly 1 z empty. C. Exactly 2 D. Exactly 3 E. Infinitely many F. None of the above 10.(1pt)Solve the systen spaces echelon Fill reduced row- 13. 1 pt)Solve the systern lets 14.(1pt)Solve equation spaces 15.(1pt)Solve the systen answer 5011 answer answer yand 37 system 21. 1 pt) Give geometric description The following svg- 7y value of h unch that the matrix linear system with infinitely many 35, value 22. 1 pt) Give geometric description Ethe following 4x+12y+kx=1 nof equations [7]1 2x + unknown constants consider th 2r 2x above sys- 23. pt) Give geometric description the following how mayy tems e fequations values 15y following sys- EXERCISES Instructions You will need to record the results of your MATLAB session to generate your lab report. Create a directory (folder) on your computer to save your MATLAB work in. Then use the Current Directory field in the desktop toolbar to change the directory to this folder. Now type diary lab1.txt followed by the Enter key. Now each computation you make in MATLAB will be save in your directory in a text file named lab1.txt. When you have finished your MATLAB session you can turn off the recording by typing diary off at the MATLAB prompt. You can then edit this file using your favorite text editor (e.g. MS Word). Lab Write-up: Now that your diary file is open, enter the command format compact (so that when you print out your diary file it will not have unnecessary spaces), and the comment line % MAT 343 MATLAB Assignment # 1 Put labels to mark the beginning of your work on each part of each question, so that your edited lab write-up has the format % Question 1 . . % Question 2 (a) Final Editing of Lab Write-up: After you have worked through all the parts of the lab assignment you will need to edit your diary file. • Remove all typing errors. • Unless otherwise specified, your write-up should contain the MATLAB input commands, the corresponding output, and the answers to the questions that you have written. • If the question asks you to write an M-file, copy and paste the file into your diary file in the appropriate position (after the problem number and before the output generated by the file). • If the question asks for a graph, copy the figure and paste it into your diary file in the appropriate position. Crop and resize the figure so that it does not take too much space. Use “;” to suppress the output from the vectors used to generate the graph. Makes sure you use enough points for your graphs so that the resulting curves are nice and smooth. • Clearly separate all questions. The questions numbers should be in a larger format and in boldface. Preview the document before printing and remove unnecessary page breaks and blank spaces. • Put your name and class time on each page. Important: An unedited diary file without comments submitted as a lab writeup is not acceptable. 1. Entering matrices: Enter the following matrices: A = [ 2 6 3 9 ] ; B = [ 1 2 3 4 ] ; C = [ −5 5 5 3 ] 2. Check some linear algebra rules: (a) Is matrix addition commutative? Compute A + B and then B + A. Are the results the same? (b) Is matrix addition associative? Compute (A + B) + C and A + (B + C) in the order prescribed. Are the results the same? (c) Is multiplication with a scalar distributive? Compute (A + B) and A + B, taking = 5 and show that the results are the same. (d) Is multiplication with a matrix distributive? Compute A(B + C) and compare with AB + AC. (e) Matrices are different from scalars! (i) For scalars, ab = ac implies that b = c if a ̸= 0. Is that true for matrices? Check by computing AB and AC for the matrices given above. (ii) In general, matrix products do not commute either (unlike scalar products). Check if AB and BA give different results. 3. Create matrices with zeros, eye, ones, and triu: Create the following matrices with the help of the matrix generation functions zeros, eye , ones, and triu. See the on-line help on these functions if required (i.e. help eye) M = [ 0 0 0 0 0 0 ] ; N =   5 0 0 0 5 0 0 0 5  ; P = [ 3 3 3 3 ] Q =   1 1 1 0 1 1 0 0 1  : 4. Create a big matrix with submatrices: The following matrix G is created by putting matrices A, B, and C from Exercise 1, on its diagonal and inserting 2×2 zeros matrices and 2×2 identity matrices in the appropriate position. Create the matrix using submatrices A, B, C, zeros and eye (that is, you are not allowed to enter the numbers explicitly). G =   2 6 0 0 1 0 3 9 0 0 0 1 0 0 1 2 0 0 0 0 3 4 0 0 1 0 0 0 −5 5 0 1 0 0 5 3   5. Manipulate a matrix: Do the following operations on matrix G created above in Problem 4. (a) Extract the first 4×4 submatrix from G and store it in the matrix H, that is, create a matrix H =   2 6 0 0 3 9 0 0 0 0 1 2 0 0 3 4   by extracting the appropriate rows and columns from the matrix G. (b) Replace G(5,5) with 4. (c) What happens if you type G(:,:) and hit return? Do not include the output in your lab report, but include a statement describing the output in words. What happens if you type G(:) and hit return? Do not include the output in your lab report, but include a statement describing the output in words. (d) What do you get if you type G(7) and hit return? Can you explain how MATLAB got that answer? Try G(16) to confirm your answer. (e) What happens if you type G(12,1) and hit return? (f) What happens if you type G(G>5) and hit return? Can you explain how MATLAB got that answer? What happens if you type G(G>5) = 100 and hit return? Can you explain how MATLAB got that answer? (g) Delete the last row and the third column of the matrix G. 6. See the structure of a matrix: Create a 20 × 20 matrix with the command A = ones(20); Now replace the 10 × 10 submatrix between rows 6:15 and columns 6:15 with zeros. See the structure of the matrix (in terms of nonzero entries) with the command spy(A). Set the 5 × 5 submatrices in the top right corner and bottom left corner to zeros and see the structure again. NOTE: Use semicolon to suppress the output for all the matrices in this problem. In your labwrite up include the pictures obtained with the spy command. To include the pictures, open your diary file using a word processor such as MS Word then, on the MATLAB figure, select “Edit” and “Copy Figure”, and paste the picture into the Word file. Make sure you crop and resize the picture so that it does not take up too much space. 7. Create a symmetric matrix: Create an upper triangular matrix with the following command: A = diag(1:6) + diag(7:11, 1) + diag(12:15, 2) Make sure you understand how this command works (see the on-line help on diag). Now use the upper off-diagonal terms of A to make A a symmetric matrix with the following command: A = A + triu(A,1)' This command takes the upper triangular part of A above the main diagonal, flips it (transpose), and adds to the original matrix A, thus creating a symmetric matrix A. See the on-line help on triu. 8. Do some cool operations: Create a 10×10 random matrix with the command A = rand(10); Now do the following operations: (a) Multiply all elements of A by 100 and store the result in the matrix A. Then round off all elements of the matrix to integers with the command A = fix(A). (b) Replace all elements of A that are less than 10 with zeros (Hint: see exercise 5(f)) (c) Replace all elements of A > 90 with infinity (inf) (d) Extract all 30 ≤ aij ≤ 50 in a vector b, that is, find all elements of A that are between 30

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