15. w = (4,5,6); V₁ = (2,-1,4), V2 = (3, 0, 1), V3 = (1,2,-1)
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- In Problems 21–26, decompose v into two vectors v1 and v2 , where v1 is parallel to w, and v2 is orthogonal to w. 25. v = 3i + j, w = - 2i - jIn Problems 2 to 4, find out whether the given vectors are dependent or independent; if they are dependent, find a linearly independent subset. Write each of the given vectors as a linear combination of the independent vectors.2. (1, −2, 3), (1, 1, 1), (−2, 1, −4), (3, 0, 5) 3. (0, 1, 1), (−1, 5, 3), (1, 0, 2), (2, −15, 1)4. (3, 5, −1), (1, 4, 2), (−1, 0, 5), (6, 14, 5)Can you help me find the unique vector described in problem 2?
- If u = < 3 , 9 > and v = < -3, 1 >, find 1/3u - 2v. (this is a vector problem)So, how would I find the vector of 3v in this problem?In Problems 40–45, use the vectors v = 3i + j - 2k and w = - 3i + 2j - k to find each expression. 40. 4v - 3w 41. || v - w || 42. || v || - || w || 43. v * w 44. v . (v * w) 45. Find a unit vector orthogonal to both v and w.
- In Problems 45–50, find the unit vector in the same direction as v.45. v = 5i 46. v = - 3j 47. v = 3i - 6j - 2k 48. v = - 6i + 12j + 4k 49. v = i + j + k 50. v = 2i - j + kThis question is regarding vectors and matrices, what do I match these 4 parts with when the 5 choices to match with are: It equals 1 It is meaningless It equals 0 It equals 4 It equals the zero vectordeal with the problem of solving Ax = b when det A = 0.22.Suppose that, for a given matrix A, there is a nonzero vector x such that Ax = 0. Show that there is also a nonzero vector y such that A*y = 0.
- In Problems 23–25, use the vectors u = 2i - 3j + k andv = - i + 3j + 2k.23. Find u * v.24. Find the direction angles for u.25. Find the area of the parallelogram that has u and v asadjacent sides.Let A =[ 4 -1 2 , -1 8 3 ,1 -2 5 ] b=[1 ,-2,3] and initial vector x 0=[0,0,0,0] perform two itearation of the gauss seidel methodLet x and y be linearly independent vectors in R2.If | |x | |= 2 and | |y | | = 3, what, if anything, can weconclude about the possible values of |xTy|?