Find all (a, b, c, d) in R* such that the given set is orthogonal. What is the value for a? {(1, 2, 1, 0), (1, -1, 1, 3), (2, -1, 0, -1), (а, b, с, d)}

Q: Find a vector å with representation given by the directed line segment AB, for A(0,3,1) and B(2,3, –…

A: We have to find the vector and draw it.

Q: Determine k so that the vectors (1, –1, k – 1), (2, k, –4), (0, 2, + k, – 8) in R³ linearly…

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Q: orthogonal

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Q: Prove that if ||u|| = ||v||, then u + v and u- v are orthogonal.

A: Given ||u||=||v||

Q: Select the orthogonal projection of (1,1,1) onto the span of (1,0,1) and (1,1, – 1) in R. O (2, 1,…

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Q: Find the norm of the vector U(2,-6,1)

A: See the solution below.

Q: Find a vector a with representation given by the directed line segment AB. A(0, 4, 2), B(4, 4, –1)…

A: Given vectors

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…

Q: Find a vector a with representation given by the directed line segment AB. A(3, 0, -4), B(3, 4, 4)…

A: The given points are: A3, 0, -4, B3, 4, 4 Vector AB can be represented as vector is AB so the tail…

Q: 5. Determine the number of vectors (x1,...,x„), such that each x; is either 0 or 1 and i=1

A: (x1,x2,...,xn) is a vector with xi is either 1 or 0.  Now, ∑i=1nxi ≥ k implies at least k of the…

Q: Show that if S = {v1,v2,.., Vn} is an orthogonal set of vectors, then for any scalars a1, a2, ... ,…

A: If S is an orthogonal set of vectors then to deduce that for any scalars set T is also an orthogonal…

Q: Find a vector a with representation given by the directed line segment E A(0, 3, 2), B(5,3, -5) Draw…

A: We need to find the equation from A(0, 3, 2) and B(5, 3, -5).

Q: Find b and c so that  (9, b, c)  is orthogonal to both  (1, 2, 7)  and  (1, −2, 1).

A: To find b and c so that (9, b, c) is orthogonal to both (1, 2, 7) and (1, −2, 1).

Q: Prove that (i) the three points A(1, 4, 2), B(3, 2, 4) and C(5, 0, 6) are collinear, (ii) the four…

A: (1) Given points are A(1, 4, 2), B(3, 2, 4) and C(5, 0, 6)

Q: Show that if S = {v1,v2,..., Un} is an orthogonal set of vectors, then for any scalars {qjv1,a2V2,…

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Q: Prove that the set of vectors B = {(1,2,3), (3,2,1),(0,0,1)} is linearly independent and spans R³.

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Q: 1. Show that the set as; S = {(1,1,1), (2,3,3), (0,1, 2)} spans R3, write the vector (4, 6, 7) as a…

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

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Q: Let ā = (1,2),b = (x,y) and = (1,-2) find the value of x and y such that a is %3D %3D %3D orthogonal…

A: Given that a is orthogonal to b So a·b=0also we have c·b=2

Q: Show that the vectors v, = (0, 3, 1, -1); v =(6, 0, 5, 1); v (4, -7, 1, 3) form a linearly dependent…

A: Given vectors v1 = (0, 3, 1, -1); v2 = (6, 0, 5, 1); v3 =(4, -7, 1, 3) . Let c1. v1 + c2. v2 + c3.…

Q: Find the projection of u onto v if, u= (4, 2), v = (5, -2).

A: Given, Formula for the projection of u onto v is given by

Q: Find a vector a with representation given by the directed line segment AB, where A(-4, 0, 1) and…

A: A=-401,  B=18-1 the vector a is given by  a=B-A

Q: Determine whether the given vectors (1, 1,-1, 1), (1,-1, 2,-1), (3, 1, 0, 1) in R* are lincarly…

A: Given vectors are: (1, 1, -1, 1) , (1, -1, 2, -1) , (3, 1, 0, 1) We have to determine whether the…

Q: - Show that the vectors X, - () 5e3t and X2 = ) 2et 7et form a linearly independent set.

A:

Q: Show that if R" = Span(v1, v2, · .· Vk) for some vectors v; of R" with k > n then one can find n…

A: Given:           If            ℝn = Span(v1,v2,..........vk) for vi of ℝn  with k>n, Prove:…

Q: 3. Show that the vectors v = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

A: Given the three vectors

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

A:

Q: find the projection of u along v u = (2, 5), v = (1, 1)

A: u=2,5 and v=1,1

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

A:

Q: Find the projection of u along v. u =〈2, -3〉, v =〈1, 2〉

A: Given: u =〈2, -3〉, v =〈1, 2〉 To find the projection of u along v

Q: Let ů,v,,v2,,v, be nonzero real valued vectors in R', such that ū is orthogonal to each v. Show that…

A:

Q: Let u = (1,2,3) and v = (2a,2a,a2) Which of the following values of a ensures that u and v are…

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

A:

Q: Find a maximal set of linearly independent vectors out of the set {v1 = (1,2, 3, 4), v2 = (2, 3, 4,…

A: From given set of vectors we have to find maximal set of linearly independent factors. Concept: Let…

Q: Let u = (k, 2 − k, −1), v = (2k, k, 3). Find k such that u and v are orthogonal.

A: Let u = (k, 2 − k, −1), v = (2k, k, 3)

Q: Show that the vectors v, = (0, 3, 1, -1); v, =(6, 0, 5, 1); v; = (4, -7, 1, 3) form a linearly…

A:

Q: Let u = (1,2, –1,5), v = (0, 1, 1,0,) and w = (3, 4, –2, 15). Show that u , v and w are linearly…

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Q: Find all values of c so that (2, 1, c) and (c – 1, 2, 2c) orthogonal. are

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Q: Determine k so that the vectors (1,–1, k - 1), (2, k,-4) and (0, 2 +k,-8) in R linearly independent.…

A: The detailed answer and explanation is given below:-

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

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Q: if u=(1,0,0) and v=(0,1,0), u and v are orthogonal Select one: True False

A: If dot product of two vector is zero then vectors are orthogonal

Q: Find the vector v in the plane represented by the directed line segment from (4,-3) to (-2,6)

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Q: Verify that (u,,u2} is an orthogonal set, and then find the orthogonal projection of y onto Span…

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Q: Consider the set of vectors {u" ,v ,w° } in R°, where u =(4,-4,8), v =(9,6,3) and w =(-9,-21,k),…

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Q: Let →a=⟨−8,6⟩ and →b=⟨0,2⟩ Compute the following vector projections. proja→ b=   projb →a=

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Q: 2- Show whether the set of vectors S={ ,,} is a basis of R3 ?

A: Given the set of vectorsS={<3,2,2>,<−1,2,1>,<0,1,0>}

Q: 11. Assume u=(1,0,0,-1), v1=(3,2,7,3), v2=(2,1,3,2), and v3=(5,2,9,5). Show that u is in the…

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Q: Find a vector a with representation given by the directed line segment AB. А(О, 3, 2), в(1, з, -5)…

A: Consider the given line segment AB→. A(0,3,2) and B(1,3,-5). Let AB→ be  a vector from A to B and…

Q: Find a vector a with representation given by the directed line segmer (-6,0, 3) and B(1,8, –1).

A:

Q: Let u= (2, 1, –1) v- -4,3α + β, 2) w- (α, 0, 2β) Find the values of a and B such that u is parallel…

A: Given, u=2,1,-1v=-4,3α+β,2w=α,0,2β