EX 1BCalculate the table G¹, n>2, where1 x y zv01 น0 0 1 w0001Gand to continue to be applied for n=2023 kαi x=1, y=-2, z=0, u=2=v, w=3.write the matrix G in the form G =I+Q and then apply the binomial expansion for commutative matrices, that is, ifAB=BA, then22(A + B)" = (2) An-kBk).k=0

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Answered: EX 1B Calculate the table G¹, n>2,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The amount of growth of plants in an ungrazed pasture is a function of the amount of plant biomass already present and the amount of rainfall.t For a pasture in the arid zone of Australia, the following formula gives an approximation of the growth. Y = -55.12 - 0.01535N - 0.00056N? + 3.946R Here Ris the amount of rainfall, in millimeters, over a 3-month period, Nis the plant biomass, in kilograms per hectare, at the beginning of that period, and Y is the growth, in kilograms per hectare, of the biomass over that period. (For comparison, 100 millimeters is about 3.9 inches, and 100 kilograms per hectare is about 89 pounds per acre.) Now we consider the amount of growth Y as a function of the amount of plant biomass N already present. (a) First we assume that the rainfall is 80 millimeters, so R = 80. (1) Find a formula for the growth Y as a function of the amount N of plant biomass already present. kg/ha (ii) Make a graph of Y versus N. Include biomass levels N from 0 to 800 kilograms…
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III. Used series of Elementary Row/Column Operations transform matrix given below into Row-Echelon Form (REF) or Reduced Row-Echelon Form (RREF). Fill in the blank box with the elementary operations for the given step and the corresponding result matrix. Use the word "over" without a space between the numerator and denominator to indicate the fraction bar or vinculum. Also, for the interchange symbol, write the word "interchange" with no spaces between the rows to be exchanged. For example, R2 is written as R2-2R1 R1 is written as (4over3)R1; -R2 is written as (-(1 over2)) R2; and R2-2R1 or -2R1+R2; and R2 R1 is written as R2interchangeR1. 3 [2 8 4 17) 2 14 5 1 5 10 -1 1. Elementary operations Step 1. Step 2. Step 3. Step 4. Step 5. Step 6. Step 7. Step 8. Step 9. Resulting Matrix UU OOL
The matrix A = (13¹) is closely related to the imaginary number i. (a) Calculate A², A³, A4, expressing each as a multiple of either A or the identity matrix I. Infer the general pattern for A4, A4n+1, A4n+2 A4n+3, where n is an integer, and notice how this compares to powers of i (b) The exponential of a matrix is defined in terms of the power series eX = 1 + X + ² X ²X² + ²/1 ² Calculate e, evaluating the series to obtain a simple 2 x 2 matrix. Explain the result geometrically, noting the close analogy with e ·X³+.

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