Question

1. Let A 1 2 3 1 2 1 (a) Compute l|Alli Allo AF b) Write out the first three steps of the power method for A with the initial vector [1,o,oT. (c) Find a QR decomposition for A. (d) Find (e) Compute the condition number Ro(A) corresponding to oo-norm. an orthogonal projection whose range is spanned by the first two columns of A.

Answer 1

slit 1 2 aij Colum n om V2 2 (33 ソー "凸 ろ, %) 6,

1 231 5 t2- 0 6 t2+06 多 3 3%

12多 121 11%)! + 212 17-80一 9 2/2-26) 23ユ 11ナ

18 1-1 t 32 52-2442 6o-W2, 6o-42 38-16 32-242 3 33-162 2-2G 33-16 3-16V (2-2 ugl 2-22 A: 20-222017 , スア 00 CO リ3

(d 24y 429- 14 1 6 2. to m 0 3333 -03 03333 O s 5

ヅ -to, 3333 ,0,5+0.5