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11 0 10 0 1 1 0 Find the eigenvalues and the corresponding eigenvectors of the matrix 0 0 2 0 Lo 0 0 2]
- 4y = 71 +et+ sin(2) a. Find the general solution b. Find a solution such that y(0) = 0, 7(0) = 1. - 7
Let {et} denote a white noise process from a normal distribution with E[et] = 0, Var(et) = σe2 and Cov(et, es) = 0 for t ≠ s. Define a new time series {Yt} by Yt = et + 0.6 et -- 1 – 0.4 et – 2 + 0.2 et – 3. 1. Find E(Yt ) and Var(Yt ). 2. Find Cov(Yt , Yt – k) for k = 1, 2, ...
1 00] 11 0 -1] 6. Suppose L = 0 1 0, U = 0 1 2 and b = 2. Solve LUX =b for x. Only half 2 LO 0 1 credit if you first find the product LU as part of your solution. que
(b) Suppose that {Y, is generated according to Y-10+ et--et-it īet-2,with et ~ N(0, 1) covariance function for (Y). Is (Y) stationary? ustify your answer. (ii) Determine ρ1 and ρ2 (iii) Using (ii) or otherwise, determine oil and ф22
11 0 -1 21 Let the reduced echelon form of matrix A = 1 - i 2 -3 0 0 0 0 LO 0 0 0 1 a) Find the determinant of A. b) Show that the columns of A are not independent. c) Find the dimension and the bases for the null space of A.
find the eigen space of 4a and 4c
Find the characteristic equations of the following matrices 4. (a) 「 4 0 1 -2 1 0 -2 0 1 (b) [3 0-5 1 1-2 11 1-2 0 (c) 19 5 -4 (d) -1 0 11 -1 3 0 -4 13 1 (e) 5 0 11 ind bases for the eigenspaces of the matrices in Exercise 4 6.
Find the characteristic equations of the following matrices 4. (a) 「 4 0 1...
-C et te Find the arclength along y = from x = 0 to x = 1. 2
1. The most stable conformation of trans-3-ethyl-1-iodocyclohexane is a. Et b. C. d Et Et 2. a 3. Which of the following is NOT a resonance structure of ozone? b. a. d. All are valid resonance structures C. 4. Arrange the following bicyclic alkenes in order of increasing stability (least stable to most stable) II II d. Il<lll< C. I<ll<llI b. I<lll<ll a. Ill<ll< 5 What is the correct Lewis structure for CHsNCO? b. No 0 НС H,C- a. d....
1 A= 11 3 0 0 0 0 0 0 0 0 1 LO 0 0 0 ro 0 0 LO 1 1 0] 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 LO 0 0 C = 11 0 0 0 Which of the matrices below is the reduced row echelon matrix A. Matrix A and B B. Matrix A and C C. Matrix B and C D. All matrices...