Question

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

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Answer 1

@0 Answers Given linear system i tiq +413=0 q1, tig - 5. A i + lią - 13 9.2 in matrise form AX - B - Az B = X 5.4 2 -1 9.2 Applying Gauss elimination method Augmented matrix matrix [118] 2 5.A 2 - - 9.2 Rq-QR, Rq and R₃-R, R₂ - 4 -3 -7 5,4 1 9.2 Rq/-3 Rq 4 o 3 -1.8 - -5 9.2

R,- R₂ > Ri and Rz - R₂ R₃ 1.8 ale alles o -). -1.8 o -22 11 R31-2275 7 کیا alor 1.8 o الامر -1.8 1 -1.5 지 & Roß, and Ry - 2 / 3 Rz Rz o o 4.3 O 0 1.7 1,= 4.3 iq=1.7 o -1.5 iz - -1.5 Q-2 ans Ax= xx AE -1 2 2 14- U - l-d O 3 18 А 0 2 2ad (1-1) [(2-1)(1-1)-8)] 0 +(-1)(2x3) = (1-4) [12-31-6] - 6 E-M3+ AM? +31-12 =0

dia = A, de=-3. dq=3 dq=3 = Eigen values To find eigen rectors a x=4 o - 3 - 3 Hz 4 2 43 2 -34, -H3 =0 34,-342 takz=0 222 - 243=0 Let - *3=xqt, M=- 3*, 47- . 11231 t b) = -3 1+3 o 3 143 4 Btz 0 o 2 (173), -H3=0 34, +(143JH₂ + Alz=0 242 +(3+2) Hz=0 Hy=t, H₂ = - 4 / 4 (3+2) = 1 + 22 (-1480) Let L' VE — - الامم

C) А- 3 {-3 | — — О ИЗ (1-3) и, — -0 1 31. – Сг-3 Jх, +4х3 -0 + (9-3 Jжа =0 9 м. Let * * * 1 м. - 4 --+3) М., — я 1-3 1-3 у T