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Problem l: Let u, v and w be three vectors in R3 (a) Prove that wlv +lvlw bisects the angle betwe...
Q6. Let W be the subspace of R' spanned by the vectors u. = 3(1, -1,1,1),...
Q6. Let W be the subspace of R' spanned by the vectors u. = 3(1, -1,1,1), uz = 5(–1,1,1,1). (a) Check that {uj,uz) is an orthonormal set using the dot product on R. (Hence it forms an orthonormal basis for W.) (b) Let w = (-1,1,5,5) EW. Using the formula in the box above, express was a linear combination of u and u. (c) Let v = (-1,1,3,5) = R'. Find the orthogonal projection of v onto W.
41 and w be vectors, and 39-42 Properties of Vectors Let u, V, and w be...
41
and w be vectors, and 39-42 Properties of Vectors Let u, V, and w be ved let c be a scalar. Prove the given property. 39. u. v = v.u 40. (cu) v = c(u.v) = u • (cv) 41. (u + v). w = uw + v.w 42. (u - v)•(u + v) = | u |2 - 1 v 12
5. (a) Let u 1,4,2), ,1,0). Find the orthogonal projection of u on v (b) Letu...
5. (a) Let u 1,4,2), ,1,0). Find the orthogonal projection of u on v (b) Letu ,1,0), u(0,1,1), (10,1). Find scalars c,,s such that 6. (a) Find the area of the triangle with vertices , (2,0,1), (3, 1,2). Find a vector orthogonal to the plane of the triangle. (b)) Find the distance between the point (1,5) and the line 2r -5y1 (i) Find the equation of the plane containing the points (1,2, 1), (2,1, 1), (1, 1,2). 7. (a) Let...
5. Let ū and w be vectors in R3. Prove that (ö - w) x (v...
5. Let ū and w be vectors in R3. Prove that (ö - w) x (v + 2) = 2(vx w).
linear alegbra Let u, v, w be linearly independent vectors in R3. Which statement is false?...
linear alegbra
Let u, v, w be linearly independent vectors in R3. Which statement is false? (A) The vector u+v+2w is in span(u + u, w). (B) The zero vector is in span(u, v, w) (C) The vectors u, v, w span R3. (D) The vector w is in span(u, v).
1. Let u - (1,1,2), v = (1,2,1), and w (2,1,1) in R. and consider •...
1. Let u - (1,1,2), v = (1,2,1), and w (2,1,1) in R. and consider • the parallelogram B = {s(3v) + t-w) 0 <s,t<1, s,te R} spanned/formed by the vectors (3v) and (-w), and • the parallelepiped P = {ru + s(3v) + (-w) 0 <T,,t<1, r, s, t€ R} [10] spanned formed by vectors u. (3v). and (-w) We take the parallelogram B as a base of P. (a) Does the ordered vector triple (v xw, 3v, -w),...
25 and 27 please 24. u i, v i+j, w i+j+k 36. L 25-26 Use a...
25 and 27 please
24. u i, v i+j, w i+j+k 36. L 25-26 Use a scalar triple product to find the volume of the parallelepiped that has u, v, and w as adjacent edges. 37. W u = (2,-6, 2), v 〈0, 4,-2), w = (2, 2,-4) to 38. S the vectors lie in the same plane. u=51-2j + k, v=4i-j + k, w=i-j ide 28. Suppose that u (v X w)3. Find (a) u" (w × v) (c)...
Let uj = [1,1,1]* and u2 = [1,2,2]t be vectors in R3 and V be the...
Let uj = [1,1,1]* and u2 = [1,2,2]t be vectors in R3 and V be the vector space spanned by {u1, U2}. a. 6pt Use Gram-Schmidt orthogonalization to find an orthonormal basis for V. b. 4pt Let w = [1,0,1)+. Find the vector in V that is closest to w.
Problem #5: (a) Let u = (10, 4, -1, 8) and v = (-5, 10, -6, -1). Find ||u - proj,u||. Note: You can partially check you...
Problem #5: (a) Let u = (10, 4, -1, 8) and v = (-5, 10, -6, -1). Find ||u - proj,u||. Note: You can partially check your work by first calculating proj^u, and then verifying that the vectors projyu and u proj^u are orthogonal (b) Consider the following vectors u, v, w, and z (which you can copy and paste directly into Matlab). u -8.9 -9.8 -5.8], v = [0.8-4.1 -3.71, w = [8.6 -9.1 -8.11, [3.4 4.8 3.11 z...
answer this . will rate after Given the vectors u = (1, -2,1), v= {5,–4,0) and...
answer this . will rate after
Given the vectors u = (1, -2,1), v= {5,–4,0) and w = (3,0,-2) (6 points) a) Graph u, v, and was position vectors and label each vector. Show your calculation or justify your reasoning (4 points) b) To the nearest degree, what is the angle between the vectors u and w. (6 points) c) Write the equation of the plane containing the vectors u and w (4 points) d) Determine if the vectors u,...
Q6. Let W be the subspace of R' spanned by the vectors u. = 3(1, -1,1,1), uz = 5(–1,1,1,1). (a) Check that {uj,uz) is an orthonormal set using the dot product on R. (Hence it forms an orthonormal basis for W.) (b) Let w = (-1,1,5,5) EW. Using the formula in the box above, express was a linear combination of u and u. (c) Let v = (-1,1,3,5) = R'. Find the orthogonal projection of v onto W.
41
and w be vectors, and 39-42 Properties of Vectors Let u, V, and w be ved let c be a scalar. Prove the given property. 39. u. v = v.u 40. (cu) v = c(u.v) = u • (cv) 41. (u + v). w = uw + v.w 42. (u - v)•(u + v) = | u |2 - 1 v 12
5. (a) Let u 1,4,2), ,1,0). Find the orthogonal projection of u on v (b) Letu ,1,0), u(0,1,1), (10,1). Find scalars c,,s such that 6. (a) Find the area of the triangle with vertices , (2,0,1), (3, 1,2). Find a vector orthogonal to the plane of the triangle. (b)) Find the distance between the point (1,5) and the line 2r -5y1 (i) Find the equation of the plane containing the points (1,2, 1), (2,1, 1), (1, 1,2). 7. (a) Let...
5. Let ū and w be vectors in R3. Prove that (ö - w) x (v + 2) = 2(vx w).
linear alegbra
Let u, v, w be linearly independent vectors in R3. Which statement is false? (A) The vector u+v+2w is in span(u + u, w). (B) The zero vector is in span(u, v, w) (C) The vectors u, v, w span R3. (D) The vector w is in span(u, v).
1. Let u - (1,1,2), v = (1,2,1), and w (2,1,1) in R. and consider • the parallelogram B = {s(3v) + t-w) 0 <s,t<1, s,te R} spanned/formed by the vectors (3v) and (-w), and • the parallelepiped P = {ru + s(3v) + (-w) 0 <T,,t<1, r, s, t€ R} [10] spanned formed by vectors u. (3v). and (-w) We take the parallelogram B as a base of P. (a) Does the ordered vector triple (v xw, 3v, -w),...
25 and 27 please
24. u i, v i+j, w i+j+k 36. L 25-26 Use a scalar triple product to find the volume of the parallelepiped that has u, v, and w as adjacent edges. 37. W u = (2,-6, 2), v 〈0, 4,-2), w = (2, 2,-4) to 38. S the vectors lie in the same plane. u=51-2j + k, v=4i-j + k, w=i-j ide 28. Suppose that u (v X w)3. Find (a) u" (w × v) (c)...
Let uj = [1,1,1]* and u2 = [1,2,2]t be vectors in R3 and V be the vector space spanned by {u1, U2}. a. 6pt Use Gram-Schmidt orthogonalization to find an orthonormal basis for V. b. 4pt Let w = [1,0,1)+. Find the vector in V that is closest to w.
Problem #5: (a) Let u = (10, 4, -1, 8) and v = (-5, 10, -6, -1). Find ||u - proj,u||. Note: You can partially check your work by first calculating proj^u, and then verifying that the vectors projyu and u proj^u are orthogonal (b) Consider the following vectors u, v, w, and z (which you can copy and paste directly into Matlab). u -8.9 -9.8 -5.8], v = [0.8-4.1 -3.71, w = [8.6 -9.1 -8.11, [3.4 4.8 3.11 z...
answer this . will rate after
Given the vectors u = (1, -2,1), v= {5,–4,0) and w = (3,0,-2) (6 points) a) Graph u, v, and was position vectors and label each vector. Show your calculation or justify your reasoning (4 points) b) To the nearest degree, what is the angle between the vectors u and w. (6 points) c) Write the equation of the plane containing the vectors u and w (4 points) d) Determine if the vectors u,...
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