Question

Hw help，thx！

3. Find the general solution to the given system. x 3 -1 1 1 1 - 1 X -1 1

Answer 1

3 -1 -1 The ration is x given equation , 2 ire. x = AX where 3 A= 1 ܝ The characteristic 3- equation 1-2 - -1 ^ (3-»)[(--)-1] + [v->+1] -- [-1-1+a] (3-1) (2-2) E») + (2->) + (2-2) o (2-) (--(3-2) + 2] Ñ - 3x + 2 * (2-a) [ 2-3x+2) - (2-^)(2-2)(x-1)= 1(2-2) -1 (1-2) a(2-2)(2-1) +2 - 22-1 x = 1, 2, 2 valve 2 rosu det vector of A corresponding the eigen eigen be the 24 73 3 -1 then 23 C259) 1 Hy 2₂-23 =0 324 - 22 - 33 = 234 => x 22-²3 R; +*2-23 = 2x2 24 - 22 +23 = 283 - x-22-2₂ = 0 taking, n=14, 3=4 then x = Ktky 1 213 %) = 2*7 =*()** (0) 19.00 vector corresponding the eigen be the set of eigan value 2 CS Scanned with CamScanner

be me eigen vector of A corresponding the eigin value 1 18 3 then 36) Y3 1 :. 24, -2 -2/3=0 39 - / -2 =9, 4, +4₂-Y ₂ = % Y -Y +43 = Y3 :. Y, - Yz 20 Y = " ;. *, - y2 =0 :. G is the eigen velor of A corresponding the eigen value 1. Hence, the general solution is t xit) a() ()** *5(1) CS Scanned with CamScanner