Grades: \\ X @ Safety Q X Circular ( X e OA11 (pa X G If T:R109 X Linear In X G (a) find t x Introduci X Linear trc X * Course H X New Tab X + V X eclass.srv.ualberta.ca/mod/quiz/attempt.php?attempt=12706482&cmid=6755851&page=3 : Quiz navigation Question 4 Find an orthonormal basis (ONB) for the hyperplane H which consists of all solutions of the equation 2 3 Tries remaining: (E) 1w + 1x - by - 6z = 0 Marked out of Step 1: a basis for H is given by 7 8 9 10.00 V v Flag question b1 Finish attempt b2 b3 Step 2 The Gram-Schmidt orthonormalization process applied to vectors b1, b2, b3 yields this ONB for H: a1 a2 - a3 Use a 4-function calculator to crunch numbers; enter v11 as sqrt(11). Check Last saved at 0:24:10 Save Progress Previous page Next page -3 C Q Search ENG 12:24 AM Cloudy EG X US 2023-03-30 3Circular ( X G If T:R109 X Linear In X X Grades: \\ X @ Safety Q X e OA11 (pa X G (a) find t x Introduci X Linear trc X * Course H X New Tab X + -> C eclass.srv.ualberta.ca/mod/quiz/attempt.php?attempt=12706482&cmid=6755851&page=2 : quiz navigation Question 3 The set 2 3 Tries remaining: 10 7 8 9 Marked out of v 15.00 Flag question Finish attempt ... is a basis for 4. Use the Gram-Schmidt process to produce an orthogonal basis for R4. u1 = V1 = u1 . V2 U2 = V2 u1 = (Do not scale your answer.) u1 . uj To make computations nicer, if necessary, we can scale this vector by a non-zero scalar, so that u2 = u1 . V3 u3 = V3 U1 u2 . 3 12 = (Do not scale your answer.) u1 . ul U2 . U2 -3.C Q Search -99+ EG X ENG 12:25 AM US 2023-03-30 3 CloudyGrades: \\ X @ Safety Q X Circular ( X G If T:R109 X Linear In X G (a) find t x Introduci X Linear trc X * Course H X New Tab X + V X e OA11 (pa X -> C eclass.srv.ualberta.ca/mod/quiz/attempt.php?attempt=12706482&cmid=6755851&page=2 U3 = V3 u1 . 3 uj U2 . 3 12 - (Do not scale your answer.) u1 . u1 u2 . U2 To make computations nicer, if necessary, we can scale this vector by a non-zero scalar, so that u3 = u = V4 uj . V4 1 U2 . V4 12 u3 . 4 13 = (Do not scale your answer.) uj . U1 U2 . U2 U3 . 13 To make computations nicer, if necessary, we can scale this vector by a non-zero scalar, so that u4 = Therefore, { ul, U2, U3, u4 } is an orthogonal basis for R*. To obtain an orthonormal basis, we scale each of these vectors as follows: 12:25 AM -3.C 99+ x ENG Q Search US 2023-03-30 3 CloudyGrades: \\ X @ Safety Q X Circular ( X re OA11 (pa X G If T:R109 X Linear In x G (a) find t x Introduci X & Linear trc X * Course H X New Tab X + V X F -> C eclass.srv.ualberta.ca/mod/quiz/attempt.php?attempt=12706482&cmid=6755851&page=2 To make computations nicer, if necessary, we can scale this vector by a non-zero scalar, so that u4 Therefore, { u1, u2, u3, u4 } is an orthogonal basis for R*. To obtain an orthonormal basis, we scale each of these vectors as follows: u1 u1 = U2 |U2 1| - U2 = u3 U3 = my = 1 WA = u3 Note: To enter a number of the form - type a/sqrt(n). Thus, { ul, uz, us, u4 } is an orthonormal basis for R4 Check Last saved at 0:24:53 Save Progress Previous page Next page -30C ED X ENG 12:26 AM Cloudy Q Search US 2023-03-30 3