Question

Find the eigen values and eigen vectors of the following matrices: Give each step Answers without intermediate steps will not be accepted.

Answer 1

② solution: Suppose A 1.5 2 het of A then 12 13 d be the eigen-value 1 A-d Ê l zoos 15-d 2 punya a 3 (5-d) (13-1), -4=D. » 65-SA-bata? - 4 - 0 » ? - 189 +61 +0 er.+18 t VELB)} = 4.861. 7 d = - 18. 1324 - 244 2 3 184_1805 - 187.2 VO 2- D E 9+ 2 vs .

Thus the eigen values of the matrin Aare 9+255 and 9-255 am Now, eigen vector x = (al corresponding to eigen value 9+255 is given by (A-dI) = 0 12 13-d and ToJ = [s-9-2V6 2 101=) 12 13-9-255) [as] = lo] [-4-276 2761-6071 1 2 4-216) (2) 70). Rx -> (-2-W8) RIERI P-4-216 2750, som Here rank of matrix is less than number of variables, so we take one variable as a constant from the (- 4 - 2V5 )4 +20=0" 62-vs), t My = 0. - (2+V5)n = 12 Take d = (2+rs)! 3) Viad

The eigen vector is a x = (17. f$2.972 (2+ V33) = (2+ rss Answer Now to the eigen vector y= (y corresponding the eigen value (9-255) is a (A- (- 2V8)I) Y sobre (5-9+255 ? " L 2 13-9+265) [%] = loj P-4 +215 2197-187 2 4+2557133 į (-2+15)& -R) -4+ 215 ñ T T -4 + 2vs2 + 2 2 = 0 (-2+ Vs) y + y = 0 (2-vs) 9, = Y.. Take ₂ = (2-vs) it .. The eigen vector is a Yo ) = (a to = (2+ka+ Answan

3) B supposed be the eigen value of B, then (B-DI! 20 of the o--)+ 2 =0 & G A o tad? - 16 a +36-0 - - + 1000 & 5d²_8 dts to = da = 8 + V64-100 žx5 8 [ 1-36 i Zlo 8 + 6 lo = 4 + 30 Thus the eigen value of B is given by di= 4 +36 and de a 4-21 llllll

corresponding to Now eigen vector : x = ( eigen value i is - (B-d, I) x = 0 di 1729-002 le-(4+31) olama - (43) */72 R RR +Ri 91-6 LO -CdM, - Collazo -'x - 72 = 0 = Take a = is The eigen vector is " x = ( ) [is] = [78 Anewer