Problem #1: Let A be a 2 x 7 matrix, and let B be m x n. Suppose that B A is a 18 x 2 matrix. What is the value of m? Problem #1: Just Save Submit Problem #1 for Grading Problem #1 Attempt # 1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #2: Find the matrix A (in terms of B and C) if (3AT + 5BC) I = 5A -2C (A) - (5BCT+ 2B) (B) -(5CIBI+20) (C) 2(5CTBT-20) (D) (5BICI + 20) (E) 5(5BICI-20) F) :(5CIB- 2B) (G) 5(5CB + 20) (H) 5(5BCT -2B) Problem #2: Select v Just Save Submit Problem #2 for GradingProblem #3: Solve for the matrix A in the following equation. (AT + 21) -1 -27 2 38 - 2 -26 (A) 1I 21 (B ) To 2 -4 26 (C TI 3 3 -36 1 -22 2 (G) 1 42 - 2 -28 2 (F) 3 -24 27 (H) 11 W - 30 Problem # 3: Select v Just Save Submit Problem #3 for Grading Problem #3 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #4: If a square matrix A satisfies AS - 3A - 61 =0, which of the following is equal to A-1 ? (A) = (71-42) (B) - (61 + 42 ) (C) 2 (31+ 43) (D) - (61-42) (E) - (31-42) (F) (71+ 42) (G) (31-43) ( H) - (41 + 42 ) Problem #4: Select vProblem #5: Let A and B be n x n matrices. Which of the following statements are always true? (i) (AB)2 = A2B2 (ii) If the homogeneous system Ax = 0 has infinitely many solutions then A is not invertible (iii) If AB = AC then B = C (A) (i) only (B) (iii) only (C) none of them (D) (i) and (ii) only (E) all of them (F) (ii) and (iii) only (G) (ii) only (H) (i) and (iii) only Problem #5: Select v Just Save Submit Problem #5 for Grading Problem #5 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #6: Which of the following block matrices are invertible? 0 B -Y A = 0 B O 0 (A) A only (B) A and B (C) neither (D) B only Problem #6: Select vProblem #7: Find the matrix A (in terms of B, C, and D) if (5D A B) -1 = C (A) -D-'CB (B) 5DCB (C) BCD-1 (D) -DCB (E) -BCD (F) 5BCD-1 (G) 5D CB (H) 5BCD Problem #7: Select v Just Save Submit Problem #7 for Grading Problem #7 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #8: Consider the following matrix A, and let B = A". Find b31, b32, and b33. (i.e., find the entries in the third row of -2 A = -4 4 O Enter your answer symbolically, separate your answers with a comma Problem #8: as in these examples your answers must be in the correct order Just Save Submit Problem #8 for GradingProblem #9: For what value of a do the following matrices commute? 3a N 2 A = B = -3 Problem #9: Enter your answer symbolically, as in these examples Just Save Submit Problem #9 for Grading