7) Consider R with its Euclidean inner product. Let L be the line spanned by the (:) vector 2 in R. If v = -1). which one of the following vectors is the orthogonal 8 3

Q: Show that except in degen-erate cases, (u * v) * w lies in the plane of u and v, whereas u * (v * w)…

A: Show that except in degenerate cases, (u x v) x w lies in the plane of u and v, whereas u x (v x w)…

Q: 4 4. Let S be the parallelepiped determined by the vectors p, = 0, P2 =5 and 3. 2 3 -3 0 P3 =0 and…

A: Solution of given problem is as below:

Q: Compute the orthogonal projection of 7 = proj,(v) = 4 [1] onto the line L through -4 and the origin.

A: Given:    Data is given

Q: Compute the orthogonal projection of v= 7 onto the line through 4 2 and the origin.

A:

Q: 4. For vectors v and ū in an inner product space V, prove that u´ projzu and i are orthogonal.

A: v

Q: (a) Prove that u + vand u - v are orthogonal in IR" if and only if ||u|| = ||v||. (b) Draw a diagram…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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A: Three vector a1,a2,a3,b1,b2,b3 and c1,c2,c3 will be in euclidean space ℝ3 If  a1a2a3b1b2b3c1c2c3=0…

Q: Compute the orthogonal projection of 7 = projz (7) = onto the line L through and the origin.

A: The given data is: v→=-69 To compute the orthogonal projection of v→=-69 onto the line L through -76…

Q: 2 Let L be the line in R³ that consists of all scalar multiples of the vector . Find the orthogonal…

A:

Q: Suppose that u, v, and w are vectors in an inner product space such that (u, v) = 1, (u, w) = 5, (v,…

A:

Q: Let W = span Given ỹ decompose this vector into y, in W and y, in W+. 8.

A:

Q: Which of the following cannot be defined as an inner product between two vectors (x0, Yo) and (¤1,…

A:

Q: Let U(9, 9, 2), V(9, t, 4), and W(2, 5, 8). U, V and W have the same starting point. find t for…

A:

Q: Recall that R, denotes the Sorgenfrey line. Express the basis for the topology on R,?.

A:

Q: Let y = and u = Write y as the sum of two orthogonal vectors, y, in the span of u, and y, which is…

A: Solution

Q: Find a vector a with representation given by the directed → line segment AB, where A(−5, 0, 1) and…

A:

Q: determine if the vector v is a linear combi­nation of th e remaining vectors.

A: To determine: Find if v is linear combination of remaining vectors

Q: Use vectors to prove that a parallelogram is a rectangle if and only if its diagonals are equal in…

A:

Q: 2) Consider R' with its Euclidean inner product. If M is the span in R' of the following 4 vectors…

A: SOLUTION-

Q: 2. Follow the directions of Exercise 1 using the weighted Euclidean inner product (u, v) = }u,V, +…

A: As per the company guidelines we are supposed to answer only first three subparts.Kindly repost the…

Q: 5) Suppose that the set of vectors {ỉ, 7, w} is linearly independent. Prove that Span({ū, T}) #…

A: Given that u→,v→,w→ is linearly independent. Prove Spanu→,v→≠Spanu→,v→,w→.

Q: Compute the orthogonal projection of = 3 onto the line L through -2 and the origin 2 proj, (v) =

A:

Q: Let a = (7, 10, 1) and b = (10, 3, 6) be vectors. Compute the cross product %3D ахЬ.

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Q: Show that there are no vectors u and v such that llull = 1, llvll = 2,and u·v= 3.

A:

Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

A:

Q: a) Prove that ||u + v|| = ||u - v|| if and only if u and v are orthogonal, (b) Draw a diagram…

A: a) Suppose u,v are orthogonal. Now…

Q: The set of vectors u = , and u2= are Linearly dependent having rank 1 having rank 3 Linearly…

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A:

Q: 13. Recall that nonzero vectors u and are called collinear if there exists = a nonzero scalar a such…

A: Given data:- Nonzero vectors are u→ & v→ Nonzero scalar α v→=αu→

Q: If ã = <!,2,37 and b=<5,0 -17, find the vector pojection of %3D %3D ŏ onto à.

A:

Q: What is the maximum of || Ar||∞ if ||r||∞ = 1? What is the maximum of ||Ar||2 if |-|2 = 1? For…

A: A=2123 (a) We know that Ax∞≤max∑ka1k,∑ka1k,…∑ka1k when x∞=1. Ax∞≤max2+1,2+3=5 The maximum of Ax∞ is…

Q: (9) Find a vector parameterizat1on of the line r(t) which passes through the points P = (2, –6, 4)…

A: The given points are P=(2,-6,4) and Q=(3,5,-3). We have to do vector parametrization. We subtract…

Q: Find a vector a with representation given by the directed 个 line segment AB, where A(–6, −6) and…

A:

Q: Compute the orthogonal projection of i = |0| onto W = Span 3

A: Here, u→=103v1→=012v2→=410

Q: Compute the orthogonal projection of i = onto the line L through and the origin. proj, (1) =

A:

Q: 18. Find the vector u in 2-space of length 2 that makes an angle 0 4.

A: A vector having length u→ and makes an angle θ is given by  u→ = u→cosθ i^ + u→sinθ j^

Q: | Show that the vectors 2 do not span R³ by giving a vector not in their span.

A:

Q: The set of vectors u = , and u2= are having rank 3 having rank 1 Linearly independent Linearly…

A:

Q: Show that there are infinitely many vectors in R with Euclidean norm 1 whose Euclidean inner product…

A: Dear students you have asked multiple questions. As per our policy your first question will be…

Q: The set of vectors u1 = , and u2 = are %3D having rank 3 Linearly independent having rank 1…

A: Given- The set of vectors u1=&lt;1,-1,3,-1&gt; and u2=&lt;1,-1,4,2&gt; To Check- If they are…

Q: Which of the given sets of vectors in R3, with the standard inner product, are orthogonal,…

A: a) Given, 01-1,011,200 Consider the vectors, u=0,1,-1v=0,1,1w=2,0,0 Now find the inner product of…

Q: Compute the orthogonal projection of i = 1 onto the line L through 4 and the origin. projz (5) =

A: Vector projection

Q: Use a directed line segment to represent the vector.u = (2, −4)

A:

Q: Let 12, v, w be vectors In an inner product space such that //u|| =5, ||v||=5, and (u, v) =-2. Use…

A:

Q: Show that if u + vand ủ – v are orthogonal, then the vectors u and must have the same length

A:

Q: Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by…

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Q: Use a directed line segment to represent the vector.u = (−3, −4)

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Q: Show that the lines with vector equations L1: 7 = (-2,1,0) + s(1, –1, 1), s ER L2 : 7 = (0,1,0) +…

A:

Q: 4. Show that u and v are orthogonal if and only if ||u + v||2 = ||u||2 + ||v||2. (Please avoid an…

A:

Q: Suppose that two vectors T and ỹ in R" are orthogonal, meaning their inner product satisfies ·g = 0.…

A: This is a problem of vector calculus.

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.