Calculate the system parameter matrices

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Reference no: EM13882833

Question 1:

Given the two vectors v1 = (2, 3) and v2 = (-2,-3), find the following graphically and write the result:

V1 - v2, v1v2, 375_Vectors.pngx v1, 86_Vectors1.pngx v2

Question 2:

Solve the following system using A-column-space and output space:
2x + y = 3
3x =4

Question 3:

Solve the following system using A-row-space and input space:
2x + 3y = 5
-x + 2y = 2
y = 2 + 0.5x

Question 4:

A linear transformation is applied to the image on the left and we got the image on the right. Find the applied linear transformation matrix.

1043_Matrix.png

Question 5:

A dynamic system is defined by the following set of equations:

x.1(t) = Ax (t) + bu(t)

y.(1) = cx (t-1)

Where X(t) = [x1 x2]T ∈ R2 is the system state vector, u(t) ∈ R is the system input vector, y(t) ∈ R is the system output vector, x.(t) = dx(t)/dt ≅ x(t2) - x(t1)/(t2 - t1) is the first derivative of state vector, A ∈ R2x2, and c ∈ R1x2 are the system parameters matrices.

An experiment was done to collect data and the obtained data is

t u x1 x2 y
0 0 2 -1 1.5
1 1 1.8097 -0.6042 1.5076
2 1 2.5891 1.2183 3.1983
3 1 3.2944 2.3194 4.4541
4 1 3.9325 2.9846 5.4249
5 1 4.51 3.3866 6.2032
6 1 5.0324 3.6294 6.8471
7 1 5.5052 3.7761 7.3932
8 1 5.9329 3.8647 7.8653
9 1 6.32 3.9183 8.2791
10 1 6.6702 3.9506 8.6455

Calculate the system parameter matrices A ∈ R2x2, b ∈ R2x1 and c ∈ R1x2 using the above information.

Reference no: EM13882833

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