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please show all work 1: Let 0 << 27, and set A= I cos(0) co -sin(0)...
= Let cos(6) sin(0) B - sin() cos() and 0 << 27 (i) Calculate the eigenvalues of B. Hence prove that the modulus of the eigenvalues is equal to one. (ii) Calculate the eigenvectors of B.
13-15 please!
13. a 14. 15. 0 Find the eigenspaces of A = 0 1 -1 Then diagonalize A if you can. LO 0 1 b Determine values a, b, c for matrix A = 0 -2 c to be diagonalizable. LO 0 1) For nxn matrix A and B, true or false? a. A is diagonalizable if the sum of geometric multiplicities of the eigenvalues is n b. If A is invertible, the only real eigenvalues are 1 and...
Problem 2: Let 4 1 2 5 1-1 0 3 2 0 3 2 a) Find the eigenvalues, eigenspaces of the linear operators LB, Lo. b) Using part a), find a basis for R3 that diagonalizes the linear operators c) Write B- EDE- with D a diagonal matrix. d) Find the eigenvalues, eigenspaces, and generalized eigenspaces of LA
Problem 2: Let 4 1 2 5 1-1 0 3 2 0 3 2 a) Find the eigenvalues, eigenspaces of the linear...
question 81 show all work please
81. Suppose cos(6) and is in quadrant IV. Find sin(0) and tan , (X) 82. Evaluate: co 83. Evaluate: sin(-600°)
(4) (15 marks) Repeat the Question 2 for the following matrices -3 4 0] 0 0 A -2 30 B 0 -1 0 -8 8 1 0 0 1 ū= 10 = > 3 (I) (2 mark) Find the characteristic polynomial of matrix A. (II) (1 mark) Find eigenvalues of the matrix A. III) (2 mark) Find a basis for the eigenspaces of matrix A. IV) (1 mark) What is the algebraic and geometric multiplicities of its eigenvalues. (V) (2...
4. (a Let (sin( x cos( ) dr + (x cos(x + y) - 2) dy. dz= Show that dz is an exact differential and determine the corresponding function f(x,y) Hence solve the differential equation = z sin( Cos( y) 2 x cos( y) dy 10] (b) Find the solution of the differential equation d2y dy 2 y e dx dæ2 initial conditions th that satisfi 1 (0) [15] and y(0) 0
4. (a Let (sin( x cos( ) dr...
Let y = 4 sin (3x). dy Find dx2 Choose 1 answer: O 12 cos (3x) 0 -36 sin (3x) o co 4. cos (3x) -4 sin (3x)
Recall that, for all c, = n=0 cos(x) = § 4 (-1)",21 (2n)! and sin(x) = (-1)"..2n+1 (2n + 1)! N=0 n=0 If i is defined to have the property that i = -1, show that ei cos(2) + isin(x) for any real number r.
Please show all work with clear handwriting
a)
Compute the Wrornskian of the set {e* cos 3x, ex sin 3x} b. Show that {ex cos 3x, ex sin 3x} form a fundamental solution set for y" – 2y' +10y = 0 on the interval (-00,00) and write the general solution
please explain the steps you take
2. Let M be the set of all measurable sets in R, and let d be our semi-metric, show that (M, d) is complete: If (An)1 is a Cauchy sequence (with our semi- metric d) then there is a measurable set A EM such that lim, too d(An, A) 0.
2. Let M be the set of all measurable sets in R, and let d be our semi-metric, show that (M, d) is complete:...