Symbolic answers must be entered using notation similar to the examples given below. If you enter decimal numbers for questions that indicate that a symbolic answer is required, it will be marked as zero, regardless of whether the decimal number is correct or not. Integer numbers (positive, negative, and O) are allowed. Below are some examples. Example Math Expression How to Enter the Answer 2 -3/5 infinity 2\"8+l 2+exp(5) 5*pi/9 4/7-3*ln (2) sqrt(2) 5"(l/3) sqrt(5exp(3)+2*ln(7*pi)) fac(5) Note: These labs were originally written to work with Matlab. You may use Matlab to do these assignments, but all of these labs can also be done online using Octave Online which can be found here: Octave Online Before attempting this lab you should work through Tutorial 3. Further information about the labs, including scheduled lab times and how to obtain Matlab can be found on the course web site. To avoid transcription errors, copy and paste your numerical answers from Matlab into the appropriate boxes below. Do NOT try to manually enter numerical answers, and do NOT modify the format of the numerical answers from Matlab. Just copy and paste them into the appropriate place on the answer sheet below. Problem # 1: Consider the following vector x, which you can copy and paste directly into Matlab. X:[5225454345464225362355214]' Use the reshape command to reshape the vector x into a square matrix, and then find the determinant of the resulting matrix. [ Just Save I I Submit Problem #1 for Grading Problem #1 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #2: Consider the following vectors, which you can copy and paste directly into Matlab. X = [5 2 2 5 4 5 4 3 ] ; y = [5 4 4 3 2 4 4 ] ; Use the vectors x and y to create the following matrix. 5 0 O O O O O O N 0 O 2 4 0 0 0 4 5 3 0 0 OOO O 'oooo oo u UN O O ON O O O O O O O O Such a matrix is called a tri-diagonal matrix. Hint: Use the di ag command three times, and then add the resulting matrices. To check that you have correctly created the matrix A, verify that det(A) = 1.2040e+04. Find the dominant eigenvalue of A. Problem #2: Just Save Submit Problem #2 for GradingProblem # 3: Consider the following 5 statements. 2 of the statements are false in general. Determine which 2 statements are false by testing out each statement on an appropriate matrix (like we did with the properties of determinants in Section 3.3 of the tutorial file). Note: You should not use a magic or pascal matrix for (i) or (ii) below because they have special properties not shared by other matrices. Try using rand instead. (i) If A is n X n, thenA and AT have the same eigenvalues. (ii) If A is n X n, thenA and AT have the same eigenvectors. (iii) IfA is n x n then det(Ak) : [det(A)]k (iv) If I is the n X n identity matrix, and J is an n X n matrix consisting entirely of ones, then the matrix I 7% is invertible and (I 7% )71 : I +J. (V) If I is the n X n identity matrix, and J is an n X n matrix consisting entirely of ones, then the matrix A = I 7 '1 is idempotent (i.e., A2 = A). It Don't forget that you are selecting which statements are false (you are not selecting which statements are true). (A) (iii) and (iv) (B) (ii) and (v) (C) (iv) and (v) (D) (ii) and (iv) (E) (i) and (v) (F) (iii) and (v) (G) (i) and (ii) (H) (i) and (iv) Problem #3: Select v Just Save Submit Problem #3 for Grading Problem #4: What matlab command, or combination of commands (using 25 characters or less), could be used to create the following matrix? 0 0 1 0 0 1 0 0 0 0 0 O O 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 O O O O Hint: Look for a lower triangluar matrix that is repeated many times. First try to produce that lower triangular matrix with as few characters as possible. Note that your answer must produce the given matrix Problem #4: when copied and pasted directly into Matlab Just Save Submit Problem #4 for Grading