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) Answer Format Unless otherwise noted, enter answers as: - Whole Numbers - Exact Fractions (e.g., 2/3 or -5/4) or (only when necessary): - Decimals correct to it decimal places The use of decimal numbers is discouraged because decimal numbers are subject to rounding errors, which could cost you marks! Epics: Sections 2.1-2.3, 5.1, and 5.2 in the textbook. PI'OlJlem # 1: Find the values ofa, b, and c so that det(A) : ax2 + bx + c. x *2 O A : *2 x *1 *2 *8 *1 Problem #1: -1,B,0 separate your answers with a comma Just Save Your work has been saved! (Back to Admin Page), Submit Problem #1 for Grading Problem #1 Attempt #1 Attempt #2 Attempt #3 Your Answer: -1, 8, 0 Your Mark: 2.5/3 -/X Note: Your mark on each question will be the MAXIMUM of your marks on each try. (So there is no harm in making another attempt at a partia ly correct answer.) Problem #2: (a) Find the deteIminant ofthe following matrix. 3 2 0 0 O *2 2 O 0 0 B : 1 *3 *4 0 O 3 3 1 2 0 *1 2 3 2 *2 Hint: Do a row operation rst. Problem #2(a): 17920 m |:| Your work has been saved! (Back to Admin Page), Submit Problem #2 for Grading Problem #3: Consider the following matrix. a b A = d e g Suppose that det(A) = -2. Let B be another 3 x 3 matrix (not given here) with det(B) - 2. Find the determinant of each of the following matrices. (a) a + 28 -g -2d C = b+ 2h -h -2e c + 2i -i -2f (b) D = 4A-1 BT (c) E = -BA3 (d) F = adj(B) Problem #3(a) : Problem #3(b) : Enter your answer symbolically, as in these examples Problem #3(c) : Problem #3(d) : Just Save Your work has been saved! (Back to Admin Page) |Submit Problem #3 for Grading problem #3 Attempt #1 Attempt #2 Attempt #3 Your Answer: 3(a) 3(a) 3 ( b ) 3 ( b ) 3(a) 3(b) 3(c B(c) 3 ( c ) 3 (d ) 3( d 3 ( d ) Your Mark: |3(a) 3 (a 3(a) 3 ( b ) 3 ( b ) |3 (b ) 3(c) 3(c) ww 3(c) 3 (d ) 3 (d )Problem #6: Find the eigenvalues of the following matrix 4 4 O - A = -3 Problem #6: 4,-5,0 separate your answers with a comma Just Save Your work has been saved! (Back to Admin Page) Submit Problem #6 for Grading Problem #6 Attempt #1 Attempt #2 Attempt #3 Your Answer: 4, -5, 0 Your Mark: 2/3 VX Note: Your mark on each question will be the MAXIMUM of your marks on each try. ( So there is no harm in making another attempt at a partially correct answer. )Problem #7: Consider the following matrix A (whose 2nd and 3rd rows are not given), and vector x. A = X = -8 Given that x is an eigenvector of the matrix A, what is the corresponding eigenvalue? Problem #7: Just Save Your work has been saved! (Back to Admin Page). Submit Problem #7 for Grading Problem #7 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #8: Consider the following matrix. Given that 2 = 0 is an eigenvalue of A, find a basis for the eigenspace corresponding to 2 = 0. Problem #8: Select vProblem #9: Consider the following matrix. o' A = O Find a matrix P that diagonalizes A. (A) 1 (G) 1 Problem #9: Select v Just Save |Your work has been saved! (Back to Admin Page). Submit Problem #9 for Grading Problem #9 Attempt # 1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #10: Suppose that a 2 x 2 matrix A has eigenvalues = -3 and 4, with corresponding eigenvectors [ 16] and [-s respectively, Find A2. Enter your answer Enter your matrix by row, with entries separated by commas. Problem #10: symbolically, as in these examples ". [ would be entered as a, b,c, d Just Save | Your work has been saved! (Back to Admin Page). Submit Problem #10 for Grading