Problem #1: Find the values of a, b, and c so that det(A) = ax- + bx + c. X N - O A = X -6 Problem #1: separate your answers with a comma Just Save Submit Problem #1 for Grading Problem #1 Attempt # 1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #2: (a) Find the determinant of the following matrix. 0 2 O 2 0 A = 0 3 0 3 O (b) Find the determinant of the following matrix. w 4 O 4 0 ooo woOOO B = 3 N 3 4 3 3 Hint: Do a row operation first. Problem #2(a): Problem #2(b):Problem # 3: Let A and B be n X )1 matrices. Which of the following statements are always true? (i) If det(A) : det(B) then det(A * B) : 0. (ii) If A and B are symmetric, then the matrix AB is also symmetric. (A square-matrix A is symmetric ifA : AT, i.e., A is the same as its transpose.) (iii) HA and B are skew-symmetric, then the matrix AT + B is also skew-symmetric (A square matrix is skew-symmetric ifA : 7A T, i.e., A is the same as the negative of its transpose.) (A) none of them (B) (ii) and (iii) only (C) (ii) only (D) (i) only (E) (iii) only (F) (i) and (iii) only (G) all of them (H) (i) and (ii) only Problem #3: Select v Just Save Submit Problem #3 for Grading Problem #4: Consider the following matrix. :r'mtr K's a A:d g Suppose that det(A) : *3. Let B be another 3 X 3 matrix (not given here) with det(B) : 3. Find the determinant of each of the following matrices. (d) F: adj boob I:| _ Enter your answer symbollcally, Problem bow). I:| as in these examples booomboob I:| boo: I:| Just Save Submit Problem #4 for Grading Problem #4 Attempt #1 Attempt #2 Attempt #3 YourAnswer: 4(a) 4(a) 4(a) 4(b) 4(b) 4(b) 4(C) 4(C) 4(C) 4(d) 4(d) 4(d) Your Mark: 4(a) 4(a) 4(a) 4(b) 4(b) 4(b) 4(6) 4(6) 4(6) 4(d) 4(d) 4(d) Problem #5: Consider the following matrices A = 8 X X2 Use Cramer's rule to find the solution to the equation Ax = b. Enter the values of x1, X2, and x3 (in that order) into the answer box below, separated with commas. Enter your answer symbolically, Problem #5: as in these examples Just Save Submit Problem #5 for Grading Problem #5 Attempt # 1 Attempt #2 Attempt # 3 Your Answer: Your Mark: Problem #6: Consider the following matrix. A = N 4 Let B = adj(A). Find b31, 632, and b33. (i.e., find the entries in the third row of the adjoint of A.) Problem #6: separate your answers with a comma Just Save Submit Problem #6 for Grading