11 -2 31 Let A = 2 1 k Find the value of k for which det A = -10. Your value of k should be an integer 10 -3 -k] Answer: Check Let [ 2 2 -1] A = -1 -11 ( 2 4 -1] Given that 1 is an eigenvalue of A, find a value of k so that (5.-1,k) is in the eigenspace of A corresponding to the eigenvalue I.
Let k be an integer such that the vectors and 3 are linearly dependent. What must be the value of - 1, 2 [1] [-1 Answer: 1 Incorrect. Try again Next page bus page 1 1 1] Let A = 1 -1 2 and x = 22 Lo -2 1] [3] [1] Let p = 2.9= 0 and r = 2 Lo] How many of the systems Az = p.Az =q, Az = r have at least one solution? (1)...
Let A a b cd and let k be a scalar. Find a formula that relates det(A) to k and det(A) Find det(A) det(A)-(Simplify your answer.) Find det(A) det(k)=(Simpify your answer.) Use the preceding steps to find a formula for det(A). Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answer.) O A. det[kA) = -det(A) OB. det/kA)= +det(A) O C. det/kA) - - det(A) OD. det/kA) - det(A)
els response. Let B -- [1 1 L2 2. 0 1 31 2. Find det B 1 (a) via reduction to triangular form (b) by cofactor expansion swer) in the textbox below. Only work on your blank sheets of paper. You will submit your 3 (12pt) - T-
1. Let A Idef g h i Given that det(A) 1, find det(B) where You should fully justify your answer 3 marks]
14. (1 mark) Let 4-1 = 1-1 -3 11 17 -2 , find the value of a. I c d A: 2 B: 3 C: 1 |D: -- | E: 11 15. (1 mark) Find the value(s) of k for which the matrix A= 1 -1 0 1 1 0 -1 has an inverse. -6 2 k E: all values of k| A: no value of k B: all k = 4 C: k = 0 D: k= 4
Let u = (1, 2, -1) and v = (1, 2, k). Find k such that the angle between u and V is 90°. Select one: a. k= -3 b.k=5 c.k=1 d. k= 7 e.k= -5
sin ak 2. (1) Let k be a positive integer. Find the Laurent series expansion of f(x) = at z = 0 precisely (presenting a first few terms is not sufficient). (2) Find Res[f(x), 0). (3) Is the singularity of at z = O removable ? ਵ
1 10 onvelge a636lutely, converges conditionally, or diverges. Justify your answer, including naming the convergence test you use. (1n(b) n7/3-4 (2k)! n-2 k-0 (-1)k 2k 4. (a) (10) Let* Find a power series for h(), and find the radius of convergence Ri for h'(x). Find the smallest reasonable positive integer n so that - (b) (10) Let A- differs from A by less than 0.01. Give reasons. 5. (a) (10) Let g(x) sin z. Write down the Taylor series for...
Tk 1 21 5 -5 k (a) Find the determinant of A in terms of k (b) For which value(s) of k is the matrix A invertible? (c) Let B-(k,1,2,0), (0, k, 2,0),(5,-5, k,0)) be a set of vectors in R4, and let k equal some answer you gave for part (b) of this question. Add an appropriate number of vectors to B so that the resulting set is a basis for R'
Tk 1 21 5 -5 k (a)...