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14. A vector that is normal to the graph of z=x² + y2 +7 at the point (2,1,12) is a) 4ỉ +29 – Ã b) î–2j+3ỉ c) 7î++4k d) – 6 –2j + k e) none of these
2. Which of the following pairs of vectors are orthogonal? (a) v = 3i - 2j, w = --i +2j (b) v = -2i, w = 5j (c) v = -i + 2j, w = -1 (d) v = 2i – 3j, w = -2i + 3j (e) None of these
Find a vector perpendicular to both 7 = 2î + +5k and w=4ỉ – 2j+k a) 3î +79-6 b) 1lî +189 – sł c) 4 -8j+ť d){+99–3 e) none of these
What is the matrix P (P,) for the projection of R3 onto the subspace V spanned by the vectors 0 Pi3 12 P2 1 23 - P33 3 1 4 What is the projection p of the vector b-5 onto this subspace? Pi P2 Ps What is the matrix P (P,) for the projection of R3 onto the subspace V spanned by the vectors 0 Pi3 12 P2 1 23 - P33 3 1 4 What is the projection p...
2 6 (1 point) Find the orthogonal projection of v 14 onto the subspace V of Rspanned by 6 and 8 projv(v) =
17. The standard matrix of the the linear transformation that represents projection onto the vector 1 m onto the vector (9)}{-1 9 ®}1] (0}{-1) none of these [1 2 3] 18. The matrix O O 5 can be reduced (using elementary row operations) to [2 4 0 100] [120] 1 007 (A) 0 1 0 (B) 0 1 0 (0) 0 1 0 (D) none of these LO 0 1 LO 0 0 Lo o o 19. Which of the...
5.4. Find the matrix of the orthogonal projection in R2 onto the line x1 = –2x2. Hint: What is the matrix of the projection onto the coordinate axis x1? Problem 5. Problem 5.4 on page 23. The following method is suggested: (1) Find an angle o such that the line x1 = –2x2 is obtained by rotating the x-axis by 0. (2) Convince yourself with geometry that to project a vector v onto the line x1 = –2x2 is the...
8. Find a vector perpendicular to both $22î +j+5k and 121 49 – 2j+k a)3î +79-6kb) 11î +18) - 8 c) 4 - 8ì+ỉ d)î +99 - 3Ã e) none of these
4.4.3. Find the orthogonal projection of v (1,2,-1,2) onto the following subspaces: 12 20 1-1 01 (a) the span of2 (b) the ma of the aris b3(0) the kernel of the matrix-2 Warning. Make sure you have an orthogonal basis before applying formula (4.42)! ; (d) the subspace orthogonal to a (1,-1,0,1) 4.4.3. Find the orthogonal projection of v (1,2,-1,2) onto the following subspaces: 12 20 1-1 01 (a) the span of2 (b) the ma of the aris b3(0) the...
(a) Find the orthogonal projection Pf(x) of a) i/2 onto the subspace of Question 1 (b) Express P in the form of an integral operator Pf(x)K(x,y)f(y) dy and find the kernel K(x, y)