Question 1 In a given electrical network, the equations for the currents i,,iz, i, are given...
Question 1 In a given electrical network, the equations for the currents i,, i ,, are given by 4, +1, +4ig = 0 2i, -i, + is = 5.4 4 +2i, - i = 9.2 Use Gaussian elimination method to evuate the three currents. (10 marks)
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In a given electrical network, the equations for the currents .., are given by +1 +11,0 21 - ₂ + 1 = 5.4 4+21,-1= 9.2 Use Gaussian elimination method to evaluate the three currents (10 mark Question 2 The matrix A of the system 1X = AX is given by 10 A=3 4 0 2 2 (a) Find the eigenvalues of A. (8 m (b) Determine the corresponding eigenvectors of A. (12 m 36 weet nhunted States
Q) Consider the following set of linear equations. ix-iz=i iy-iz=0 ix -iy z-1 a) Write the above system of equations in matrix form. (AX-B) b) Find x, y, z using Gauss elimination method c) Find the determinant of the coefficient matrix A.
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Use Gaussian elimination method to evaluate the three currents. Question 2 The matrix A of the system AX = 2X is given by 10-1 A = 31 4 0 2 2 (a) Find the eigenvalues of A. (b) Determine the corresponding eigenvectors of A. in United States
a) [15 marks] Write the differential equations that describe the behavior of the electrical system shown in Figure 1. Assume that all electrical components behave linearly. Note that v(t) is an external input voltage signal, and vi(t) is the output voltage signal, respectively. 0000 1H 1Ω 1Ω M v(t) Figure 1. Electrical network for question 1. Use the currents ij, iz, and iz which flow through the inductors next to the red, green, and blue arrows, respectively, as the key...
(a) Show that the system of differential equations for the currents iz(t) and iz(t) in the electrical network shown in the figure below is di2 41 + RI2 + Riz = E(t) dt di3 L2 + RI2 + Riz = E(t). dt R 13 41 i2 E ᏪᎲ L lllll L2 By Kirchhoff's first law we have the following relationship between 11, 12, and iz. 11 - 12+ iz By applying Kirchhoff's second law to the iq, iz loop, we...
Given the system of linear equations 5?1 + 2?2 + ?3 = 45 −2?1 + ?2 − 3?3 = −4 4?1 − ?2 + 8?3 = 2 a. Write the augmented matrix b. Solve the system by Gaussian elimination & backward substitution method.
The system of differential equations for the currents i1 (t) and i2(t) in the electrical network shown in the figure is dt(々 =( R2-212/ R2/L1 Use variation of parameters to solve the syster if R1 = 8 Ω, R2-3 Ω, L1 = 1 h, L2-1 h, E(t) = 150 sin(t) V i1(0) = 0, and i2(0) = 0. (i1 (t),ら(t) = R2 し2
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MUID-TERM (40 marks) Instructions: Attempt ALL qtion Show COMPLETE working Question In geven electrical network, the equations for the events i... are given by 21-5+59 1 4+39-6-07 3,2,=-3.1 Use Gaussian cumination method to evaluate the recent (10 marks) Question 2 The mate of the system XXX given by (110 =10 11 1 0 1 Find the eigenvalues of A (& marks) Determine the corresponding cige vectors of 4 (12 marks) Question 3 inted Statesi imo e 1...
dx = 1. (10pts) 3. Given the system of linear equations 5x1 + 2x2 + x3 = 45 -2x, + x2 – 3x3 = -4 (5pts) 4xy – X2 + 8x2 = 2 Write the augmented matrix b. Solve the system by Gaussian elimination & backward substitution method. 21 a. 30