2.10-3. Consider the system of Problem 2.10-2.A similarity transformation on these equations yields d 0 w(k) + B,u(k) 0 d2 w(k + 1) = y(k) = C,x(k) %3D (a) Find d, and d. (b) Find a similarity transformation that results in the A, matrix given. Note that this matrix is diagonal. (c) Find B, and C (d) Find the transfer functions of both sets of state equations to verify the results of this problem.

2.10-3. Consider the system of Problem 2.10-2.A similarity transformation on these equations yields d 0 w(k) + B,u(k) 0 d2 w(k + 1) = y(k) = C,x(k) %3D (a) Find d, and d. (b) Find a similarity transformation that results in the A, matrix given. Note that this matrix is diagonal. (c) Find B, and C (d) Find the transfer functions of both sets of state equations to verify the results of this problem.

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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Q.2. A system of equations is given: x, – 2x, –x, = 3, 3x, – 6x, – 2x, =2. (a) Write the system of equations in matrix and vector equation forms. (b) Use the Row Reduction Algorithm to solve the system. (c) Write your solution in parametric vector form and describe it geometrically. (d) Write the solution of the homogeneous system that obtain from give system of equations. 1 1 2 Q.3. Let a, = 2. a, =-2|, a, = and b = 1 3 -2 -2 (a) Determine if bis a linear combination of a,, a, and a,. (b) Determine if the vectors a,, a, and a, are linear independent.
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U and = span{[-3 4 5],[-11 -2 3]} W = span{[ span{[−4 x = [ UnW = −1 5],[-12 -1 1x×3 of V = R¹×³. Find a matrix X € V such that E 5], [-12 -5 9]} = span{X}.
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6. LADW #2.2.1bf, page 46 (you only need to do (b) and (f)) - Note that you need to solve the system and write your solution in vector form. You can use technology to help (ie, you do not need to do row reductions by hand), but you shuld show that main steps (ie, what the reduced echelon form looks like and the corresponding system of equations). 2.2.1(b) 2.2.1(f) x12x2x3 = 1 2x13x2 + x3 = 6 3x1 5x2 = 7 x1 + 5x3 = 9 2x1 2x2x3 + 6x4 - 2x5 = 1 x1x2 + x3 + 2x4 x5 = 2 4x1 - 4x2 + 5x3 +7x4 x5 = 6