Question

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

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Answer 1

E 4 -[A] 2 AX = Xx 0 = XY - XV 1=x[IV - ] = IV-VI O = 0 -1 3 1-A 4 20 D 2 21 ( - )(..) 6-1) - 8) -o-16-0) -0. (1-1) (1-1) (2-x) - 8 (1-1) - 6 =0 - 8 + 8d6=0 (1-x) (1-2) (2-1) (1-x)" (2-x) + 88-14 = 0 (1 + x² - 2X) (2-1) + 81 - 14 = 0 2-1 + 21² - x 3 - 4 1 + 2x² + 81-14 =0 - 2 + 4x + 3x - 12 = 0 x ² - 4 1² - 3X + 12 =0

X-4-2) +12 = 0 (-A)-30-60) ^, = + 1 = -3, z = 4 6+) A-I = 3 4 D -√3+2 2 X = 0 Gaussian elimination, [A- 1, I solving by R./13 +1) Ri 0 4 3 - 3+1 -√3+2 2 D Pat R₂-3R, R2 O 3+1 0 - 6+1 -38375 0 D -√3+2 2

к» («rs ) эк. х 1 Зер- о о 7 + O с 2. - +2 2 * * *at-y - 6 +2 а а g O о [3+2. 12 12 = x 1 - 2 а 3 = X Як И-- Web-

X3 = -V3 3 341 4 o 2 Ri/3+1 Ri -V3+1 0 1 O 3 3 + 1 4 % √3+2 o 2 R₂ - 3R, R2 O 313 +5 13+) 0 o 2 √3+2 R₂ R2 tesley O V3! O 0 २ 2 √3+2 o 0 -V3! D R3 - 2R₂ R₃ O 1 0 Ex x₂ = X = 2 ER -13-2x3 23

da=4 4 2 - R1-3 RI ६ 07 2 R2-3R, R2 o O -3 2 R2 0 / -) - 2 0 2 R₂ - 2 R₂ R₂ w 1 1/3 D 1 0 O a x = -xz 7.2 = 23 + x * - Ex =