Consider system i = Ax, where A is 2 x 2 matrix. Given two initial states x(0), we have two state response as follows: -3t Given z(0) = = r(t) 4e-3t 2e-2t Given r(0) = = r(t) -2t; Find matrix A.

Q: Given A = [1; 2; 3]; B = [4; 5; 6];, find the array product of the two vectors.

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Q: Given vectors T = 2a, 6a, + 3a, and S = a, + 2a, + az, find (a) the scala %3D ction of T on S, (b)…

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Q: Consider the vectors A =4ag+2ka,+az and B = ax+4ay-1baz value of k the two vectors A and B will be…

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Q: Given A -> Transfer the vector to cylindrical and spherical coordinates.

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Q: a). Assuming state vector to be write down the state space model for the system in matrix form. b).…

A: The SFG diagram of the system will be

Q: Problem 2. Consider a LTI system i = Ax + Bu, y = Cx, given specifically by -3 1 1 -3 -3 i = 1 u, x…

A: The question is based on Gilbert's test for controllability. According to it, for the system to be…

Q: Given A = Axax +Ayay + Azaz (in cartesian coordinates) and A = Apa, +Aqaq + Azaz (in cylindrical…

A: Solution :-  In above diagram it can be clearly seen that the y axis in cartesian coordinate is…

Q: 2. Compute for the triple scalar product of Ā, B, and C where А- - 2х ау — 4у az, В - (-4,5, -6),…

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Q: Consider that a third-order system has the coefficient matrices [1 A = |0 [0] B = |1 2 -1] 1 C = [0…

A: Transfer function: The transfer function is Laplace transform of output divided by Laplace…

Q: Given vectors T = 2a, – 6a, + 3a, and S = a, + 2a, + a, find: (a) the scalar projec- tion of T on S,…

A: First calculate unit vector for given two vectors.  Let unit vector of T be aT and S be as. Scalar…

Q: Transform vector 5ax-2a,-4a-, at A(x = 4, y = 6, z = 5) to cylindrical coordinates at the point…

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Q: Q2) Transform the vector:S= 2cos0 ar – System, then evaluate S at (2,0,2). 2sine a0 to cartesian…

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Q: 4. Given vectors T = 2ax - 6ay + 3az and S = ax + 2ay + az, find: (a) the scalar projection of T on…

A: (a) The scalar projection of T on S is given as: Projection=T.SS=2-12+312+22+12=-76 (b) The vector…

Q: Consider the system of equations below: dx 2x + 3y dt dy 3x + 2y dt 2) If we denote V1 and V2 as the…

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Q: Find the matrix convolution of below given sequences. k1(n) ={ 1,-1,2,3} k2 (n) ={1, -2, 3, -1}

A: According to the given question, it is required to determine the convolution of the below given…

Q: Figure 4 shows a position-control system for motion control system. Suppose that, for constant…

A: In this question,  Find the position error constant Kp  ?  Determine the value of k for the steady…

Q: Given vectors: Ā= αāx + āy +4āz B = - 3āx + ßāy − 6āz C = 5āx - 2y + yāz *** Determine a, p, and y…

A: We need to find out value of unknown for given vector for given conditions

Q: Figure 4 shows a position-control system for motion control system. Suppose that, for constant…

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Q: 4. Use Vectors to find the length of the diagonal of the parallelogram determined by (itj) and…

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Q: Given vectors A = a, + 3a, and B 5a, + 2a, - 6a,, determine (a) A + B| (b) 5A B (c) The component of…

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Q: QI) vectors A = 2 ax + 4 ay, C 6 ay - 4 az find the smaller angle between them using the cross…

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Q: A = aa, + a, + 4a. в - За, + Ва, - ба, C = 5a, 2a, + ya: determine a, ß, and y such that the vectors…

A: if the two vectors are mutually orthogonal then the  A(dot)B = 0 B(dot)C = 0 A(dotC) = 0

Q: The state-space representation of a causal LTI system is given by, õ[n + 1] = A · õ[n] + B • x[n]…

A: a) A=0129-13 , B=01C=-352429 , D=1Transfer function, H(z) = C(zj^-A)-1B+D…

Q: 1.) Given vectors A = aa, + a, + 4a, B = 3a, + Ba, - 6a, and C = 5a, - 2a, + ya, determine a, B, and…

A: The solution is given below

Q: Given the system represented in state space as follows: * -7 6 * =|-5 4 3 x+ -8] 7 y = [9 9 8]x…

A: Given X  ˙=Ax+Bu Y=Cx+Du A=-1-76-54347-85 B=-5-15 C=998

Q: Transform the vectors F 10 a, to spherical coordinates at (4, 110°, 120°)

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Q: Q2. Transfer vector D = ya, + zay to the (a) or (b) a. Cylindrical coordinate at P(p= 2, 9 = 60°, z…

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Q: Determine the values of the following products of base vectors: a) a, • a b) a, • a, с) а, х а,

A: cartesian co-ordinates can be represented by (x,y,z) and cylindrical coordinates (ρ,ϕ,z)spherical…

Q: A K Map is given below, A.B 1 1 A.B 0 0 A.BO A.B 1 1 which of the following is the simplified…

A: Given k-map:

Q: Find the y-component of the given vectors by use of the trigonometric functions…

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Q: Given vectors A = 3ax + 4ay + az and B = 2ay – 5az, find the angle between A & B.

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Q: Transfer vector D = yax + za, to the (a) or (b) a. Cylindrical coordinate at P(p=2, p = 60°, z = -1)…

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Q: -1.5 1 1 0.5 0.5 A = -0.5 0,B= 0 0.5 -3 2 1 3,

A: Considering the system is linear time invariant and the equation of the state space is represented…

Q: If vectors A = a, + a,, B = a, -az and C = 2a, + a,. Find A x B а. 2а, — а, — 2a, b. – 2az – ay +2a,…

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Q: 2. If A = 2a, + 0.3ay – 1.5a, and B = 10a, + 1.5ay – 7.5az, Show that A and B are dependent %3D…

A: Given that  A=2ax+0.3ay-1.5azB=10ax+1.5ay-7.5az It is known that, if two vectors A and B are…

Q: 2r ar + System, then evaluate S at (1,1,1). Q2) Transform the vector: S = 2 cose αθ + rsinθ αØ to…

A: Cartesian coordinate system: This system is used for locating the cartesian coordinate in the plane.…

Q: 5) Given vectors T 2a, - 6a, + 3a, and S= a,+2a, + a,, find: a) The scalar projection of T on S. b)…

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Q: SOLVE Q7 ONLY Consider the state matrix A and input matrix B given by -1 1 A = 1 -2 1 ;B= 1 1 1 -1 1…

A: Given : system matrix A and input matrix B Calculate : The uncontrollable Eigen value

Q: Find the impluse response h[n] fc invariant system given by: 1 X(z) 1 +z-1 +z-3 1 1 Y(z) %3D 4 +

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Q: Three vectors A, B and C lie on the 3D RCS. The scalar product of A and B is equal to -2. The scalar…

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Q: 5.) Given A = (10v2) ( ax+az) and B = 3( ay + a:), express the projection of B on A as a %3D vector…

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Q: If A - B = 0, is it necessarily true that A = B? (A and B are vectors) Select the correct response:…

A: Let A = Axax+Ayay+Azaz and B = Bxax+Byay+Bzaz

Q: Q2. Transfer vector C = xa, + ya,y to the (a) or (b) %3D a. Cylindrical coordinate at P(p= 2, 9 =…

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Q: Show that a – 2 B +3 y, – 2a +3 ß – y, 4a –7B+7y are collinear; where a ,ß ,7 being non coplanar…

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Q: = etermine the divergence of the vector A yxa₂ + zyay+zza, at (6.5.5). div(A) =

A: We need to find out divergence of given vector

Q: Consider the vectors A =4a,+2ka,,ta, and B = a+4a,-16a, what value of k the two vectors A and B will…

A: Need to find K value

Q: 5.) Given A = (10v2) ( ax + az) and B = 3( ay + az) , express the projection of B on A as a vector…

A: First we will find out unit vector in the direction of vector A and then we will find out dot…

Q: #A - 5,2 â, + 1,8 âg + 7.5 â, and B 4,5 à, + 6.9 ây + 2,4 âz. if Ax B =Kâ, + Lâg + Mâ, then L=?

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Q: Consider the vectors A =4ax+2ka,taz and B = ag+4ay-32a, what value of k the two vectors A and B will…

A: Orthogonal vector have dot product zero . Given vector A and B

Q: Given vectors A 3a, + 4a, + a, and B 2a, - 5a, find the angle between A and B. %3D

A: A=3ax +4ay +az B= 2ay -5az angle between A and B?