Related to maths In a given electrical network, the equations for the currents .., are given...
Question 1 In a given electrical network, the equations for the currents i,,iz, i, are given by 4+₂ +4i₂ = 0 2i, - iz + z = 5.4 i, +2i, - i = 9.2 Use Gaussian elimination method to evduate the three currents. (10 marks) Question 2 The matrix A of the system AX = AX is given by (10-1 A = 3 1 4 02 2
Related to maths 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
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)
Related to maths 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...
Differential Equations and Matrix Algebra problem: Can you please show how to do numbers 2 and 3? Could you show once you find the eigenvalues, the steps you take for the Gaussian Elimination and row reducing to get the eigenvectors? I'm having trouble with the Gaussian Elimination portion of the problem, trying to get the bottom row of the matrix to be all zeros. For problem 3, I found the eigenvectors when lambda is equal to 0, but I'm stuck...
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
Find the general solution to the system of linear differential equations X'=AX. The independent variable is t. The eigenvalues and the corresponding eigenvectors are provided for you. x1' = 12x1 - 8x2 x2 = -4X1 + 8x2 The eigenvalues are 11 = 16 and 12 = 4 . The corresponding eigenvectors are: K1 = K2= Step 1. Find the nonsingular matrix P that diagonalizes A, and find the diagonal matrix D: p = 11 Step 2. Find the general solution...
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...
Q.1 Using the method of Triangular Decomposition solve the set of equations. Xı - 2x2 + 3x3 - X4 = -3 3x1 + x2-3x3 +2x4 = 14 5xi +3x2+2x3 + 3x4 = 21 2x1 - 4x2 – 2x3 + 4x4 = -10 If Ax = 2x, determine the eigenvalues and corresponding eigenvectors of -3 0 6 4 10 - 8 A 4 5 3 B= 1 2 1 1 2 1 -1 2 3 Q.2
Given a data matrix X as in Question 2, Assume the means of the p variables are zero. Let S = 1X,X be the sample covariance matrix. Let λι > λ2 > . . . > λ, be the ordered eigenvalues of S. Let el, . . . , ep be their corresponding orthogonal eigenvectors with unit length. In multivariate analysis, we usually want to use the first few eigenvalues and eigenvectors to represent the original data, as a tool...