Question: Problem # 1: Consider the following matrix A (whose 2nd and 3rd rows are not given), and vector x. -1 -2 8 2 A =

Problem # 1: Consider the following matrix A (whose 2nd and 3rd rows are not given), and vector x. -1 -2 8 2 A = >ii1: =l P3 and T: P3 > P3 dened as so) = 12(0))? + pa: + p(1) To) = 12(2)}? + pa): + pa) Is p(x) = 3x2 5x + 2 an eigenvector of T 0 S ? If so, what is the associated eigenvalue? If p(x) is an eigenvector, then enter the associated eigenvalue into the answer box below. Otherwise enter 1 0 O 0. Problem #7: (a) Express the complex number (-2 +57) in the form a + bi. (b) Express the below complex number in the form a + bi. 7 -6i i (4 + 3i) (c) Consider the following matrix. A = 1 + 32 0+4:7 3 + 4i 3-3i Let B = A-. Find b11 (i.e., find the entry in row 1, column 1 of A-1) Problem #7(a): if your answer is a + bi, then enter a,b in the answer box Enter your answer symbolically, Problem #7(b): as in these examples if your answer is a + bi, then enter a,b in the answer box Enter your answer symbolically, Problem #7(c): as in these examples if your answer is a + bi, then enter a,b in the answer box Just Save Submit Problem #7 for Grading Problem #7 Attempt #1 Attempt #2 Attempt #3 Your Answer: |7(a 7(a) 7(a) 7(b) 7(b 7(b 7(c 7(c) 7(c Your Mark: |7(a) 7 (a) 7 (a ) 7 (b) 7 (b) 7(b) 7(c) 7(c) 7(c Problem #8: Given a matrix A with complex entries, let A* be the matrix formed by taking the complex conjugate of every entry, and then taking the transpose. For example all a 12 a11 d21 A = A* = a21 a22 a12 a22 True or False: The diagonal entries of AA* and A*A are always real numbers. Problem #8: Select Just Save Submit Problem #8 for GradingProblem #9: Consider the matrix -3i 0 -3i A = 1 1 2i 2i True or False: 0 is an eigenvalue of A. Problem #9: Select v Just Save Submit Problem #9 for Grading Problem #9 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #10: Let z = -7 + 6i and w = 3 + 9i. Find a and b such that ? = a+ bi Enter the values of a and b (in that order) into the answer box below, separated with a comma. Enter your answer symbolically, Problem #10: as in these examples Just Save Submit Problem #10 for Grading

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