(a) Verify that the roots of z-39x + 70 are 2, 5 and-7, using substitution. [1] (b) Give the eige...
Linear Algebra Question#1
y Suurěd lower Q1. Suppose that we have the twin recurrences;, bn+1 62b-48cn and cnt8b,-6m Let bo: 26 and co 16. (a) Diagonalise the underlying matrix and hence find the formulas for bk and ctk for any integer k 20. (b) Use logarithms to predict which is the smallest value of k such that both bu and ck are greater than 1,000,000 and check your answer. 2 -2 1 3 y 3 -3 1 Q2. (a) Carefully...
Please solve the following
with full steps.
2. Given the following z-transform of the impulse response h [n], of a causal LTI system Ti H1 (z) = (,-1)(z-0.5) (a) Find hin (b) Verify the first three non-zero values of hi[n] using long division. (c) Find the z transform Hs(z) of hs[n]-2"hi[n], and specify the ROC. (d) Find thez transform H4() of han+n -1], and specify the ROC. e) Find the impulse response, hs[n], of the system Ts, which is the...
1. For the matrix 5 -2 3' -1 0-1 0-2-2 -5 7 2 give a minimal spanning set for a. the nullspace of A. b. the row space of A. c. the column space of A. d. Verify that the set of all 2 x 2 upper triangular matrices with real entries form a subspace of the vector space of all 2 × 2 matrices with real entries.
1. Draw the structures of: a) (Z) 2-iodo-3-methyl-2-heptene b) cis non-3-en-5 yne Give the IUPAC name of the following compounds, including steochemistry. a) F CH2CH2Br CH3CE 2. a) Draw the most stable chair conformation of cis 1,3-difluorocyclohexane. b) Draw a Newman projection of 2-iodo-3-methylpentane looking down the 3. Compound X has the formula CoHB2Br4. Compound X reacts with excess H2/Pd to give CATHa6Bra. How many does compound X have? Show how you got your answer. rings 4. For each pair...
0 7. Let A= 71 -2 1 2 -1 -1 (1 2 2 , B= 1 -2 1 -1 10 and C= 1 -3 2 100 1 100 (a) Compute det A, det B, det C, det(AB) and det(A + B). (b) Verify that A and C are inverse matrices and use this fact to (i) solve the simultaneous equations: x – 2y + z = 2 2x – y - 2= -1 x + 2y + 2z = 3...
1) Using Matlab, find all real and complex roots of the following polynomial equation: (x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)=8 2) Using Matlab, find the root for the following system of equations. Both x and y are positive. a: (x^2)cos(y)=1 b: e^(-4x)+1
Problem # 1: (70 points) Solve the following problems (a) and (b) using Laplace Transform: a) (7 points) y(0)-y'(0)-0 y"(0)-1 b) (dX/d't) + 3 (dy/dt) + 3y-0 (7 points) (d'x/d't) +3y-te' x(0) = 0 x'(0) = 2 y(0) = 0 c) An nxn matrix A is said to be skew-symmetric if AT--A. If A is a 5x5 skew-symmetric matrix, show that 9detA)-0 (4 Points) d) Suppose A is a 5x5 matrix for which (detA) =-7, what is the value of...
please solve only part(a) and
part(b)
Problem 7. A 2 × n clockerboard is to be tiled using three types of tiles. The first tile is a white 1 x 1 square tile. The second tile is a red 2 × 2 tile and the third one is a black 2 x 2 tile. Let t(n) denote the number of tilings of the 2 × n checkerboard using white red and black tiles. (a) Find a recursive formula for t(n)...
2. Consider the following set of complex 2 x 2 matrices where i = -1: H = a + bi -c+dil Ic+dia-bi Put B = {1, i, j, k} where = = {[ctdie met di]|1,3,c,dex} 1-[ ), : = [=]. ; = [i -:], « =(: :] . (a) Show that H is a subspace of the real vector space of 2 x 2 matrices with entries from C, that is, show H is closed under matrix addition and multi-...
Can you complete my answer and verify it
thank you.
Chapter 10 Section 1 Additional Problem 1 Consider the hypothesis test Ho: Mi = u2 against H: M1 < u2 with known variances (j = 11 and 02 = 6. Suppose that sample sizes nj = 10 and n2 = 16 and that Æj = 14.4 and 12 = 19.8. Use a = 0.05. (a) Test the hypothesis and find the P-value. (b) What is the power of the test...