Question

12,0). A.) Compute 112, 43 1 201 6.) a.) Find an orthogonal basis for using the column space of D-0 2 3 1 02) b.) Make an orthonormal basis from the columns of D. c.) Find the vector (123)' as a linear combination of the orthonormal basis above.

Answer 1

0 V2 = 2 y = 4 U2 = V₂ - 5 114 11 <V2, ul. 14 <V2,447=2 114112 = <44,447 = 1+1 = 2. 4V, uz uz U3 = V, - <V3, 4 Jul 27 <V3, 44% = %, <V3,427 = 6-2 = 4. 1142112 = <42,427 = 1+4+1 = 6 C119 -1-43] 1-5/37 2- 3-4/21 = 1513 1] [2-1 +43 1/3 ç IAL 2 c 1-5/377 *- {1,4, 15/ ) is an orthogonal • 1 / 1 basis for R? (6) login? = (0,37 = 25.7***

| = 5 ,14=12, Hual G IL。 uu116 公交: . TIE] | Yai | Y5} }, | 2011 YS; voll is an orthorsmal basis from the Columns of D. ||YE」,「 |-YS Yial 完 十4, 1 | +$15 /.. 23 「是是是 造+三一言 = 1 . 2+ 点 :2 smented matrix of the above fystem is

돼 l 21 - 252 1월| 이 방이 화 7eley = 각 4 1 - + - 후 = 1 - - + 후 봉 fte=ce=%=30% 6 ~ 5부 se 5 고 10 왕 Y)에 - 2% - R3 → Gag 막 루 a at at at alee - 카 d 아하 까 هما ت یم ما 가에 이