Question 2Given1)11)111Represent the above linear system as AX= BGivenx1 + 2x2+3x3 = 52x14x2 +6x3 = 183x1-9x2-3x3 = 6[10 0L= 2 22 0[3 132 133and U =[1 2 30 1 2300 1Complete the LU decomposition for A.Find the solution for AX= B using the LU decomposition in (ii).

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Answered: Question 2 Given 1) 11) 111) x1 +…

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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Q3) A) select the correct answer:- 1-Inverse z-transform of the system can be calculated using: a) Partial fraction method b) Long division method c) Basic formula of the z-transform d) All of the mentioned 2- The ZOH is physically equivalent to:- a-D'A b- A/D c- filter 3- For jury stability test and characteristic equation is odd, the condition for stable d- both a and b. system eQ(-1) =0 , bQ(-IX0, aQ(-1)0 4- steady-state error for type two system and ramp input is equal a) 1 .b) 0.c) infinity , d) there is a value 5-The roots of characteristic equation are z = 0.244 + j0.970 a) System is stable b) system unstable, c) marginally stable Kz B) G(2) = And T-0.5 sec. (z-Xz-0.6065) 1- Find the value of(K) for the steady-state error to a unit-ramp input to be(0.25). 2- For the value of (K) found in part (a), find (C), (Wn) and (time-constant=r) of the system
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6. Prove that the Rotation Matrix R corresponding to quaternion q = (a, b, c, d) is given by 1. Ꭱ . = [2(a² +6²) - 1 2(bc + ad) 2(bd - ac) 2(bc - ad) 2(a² + c²) - 1 2(cd + ab) 2(bd + ac) 2(cd - ab) 2(a²+d²)-1]
2 -2 -21 0 -2 2] A = [-1 i) Find an LU-decomposition of A. -2 , solve the system Ax = b by using the LU obtained in i). 6. ii) If b =
where R₁1 = Blank 4, R12 = Blank 5, R13 = Blank 6, R21 = Blank 7, R22 = Blank 8, R23 = Blank 9, R31 = Blank 10, R32 = Blank 11, R33 = Blank 12.
Consider a linear system as follow.
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Apply the Gram-Schmidt process to the vectors 2 4 Vi =| 1 -4 |-2 V3 8 explain why the v,'s are linearly independent. Also use your output to make an orthonormal he three vectors w1, W2, W3 that you get from the Gram-Schmidt process should all have as a safety check you may want to verify directly that they are pairwise orthogonal.)
If A= (a;j)3×3 and B= (b;)3×3, Where aj + aji = 0 and bj – bịi = 0 Vi, j then A B³ is A) singular B) zero matrix c) symmetric D) skew-symmetric matrix
Qa) attached below Qb) attached below Qc) ? (alpha) = ? Qd) ? (beta) = ?

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Question 2 Given 1) 11) 111) x1 + 2x2+3x3 =5 2x14x2 +6x3 = 18 3x1-9х2 - 3x3 =6 Represent the above linear system as AX=B Given [10 0 L= 2 122 0 and U= 12 3 0 1 23 00 3 132 133] Complete the LU decomposition for A. Find the solution for AX = B using the LU decomposition in (ii).