(b1, b2, ..., bn) be any two vectors in R". The inner product Let a = (a1, a2, . .. , an) and b = (dot product) of these two vectors are defined as ā ·b = a1b1 + a2b2 + · · · + anbn; and also the norms of these vectors are defined as |Jā|| = Vā a = V až + a3 + |||| = V5.5 = V/bỉ + b3 + • · + an, + b%. n Prove the Cauchy-Schwarz inequality (a b)? < ||ā||2||P', that is the inequality (abı + azb2 + · ..+ anbn)² < (a? + a3 + · ..+ a (bỉ + b3 + + a)(bỉ + b3 + + b% ). ..

Q: ex/IF Ā=i-j+3k and B =2 i+6j+3K Find the vector pricâ+B) and Prj (À-B).

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Q: Can the vector (3, −5, 2) ∈ R3 be written as a linear combination of the vectors v1 = (2, −3, 1) v2…

A: Linear Combination:Let V be a vector space and S = {v1, v2, · · · vn} ⊆ V . Then for α1, α2, · · ·…

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Q: Which is the vector perpendicular to the vectors n₁ = (2, -3,0) and n2 = (1,7,9)?

A: Given that: n1→=2,-3,0, n2→=1, 7, 9 The perpendicular to the vectors n1→ and n2→ is required.…

Q: Show whether or not the set of vectors B = {U, V, W} where U = V = and W = 0 is a basis for R³.

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Q: 2 Let a = -1 | and b = 1 | be two vectors 1 What is |al2|b|2 |a · b[? ?

A: Let us consider the vector v=x1,x2,....,xn then the magnitude of the vector is obtained as…

Q: Suppose that uj and u2 are orthogonal vectors, with u1 = 2 and u2|| = 4. Find |5u1 - u2 ||. ||5u1 -…

A: We have to solve given problem: Let  U1=(a1,a2)  U2=(b1,b2)5U1-U2=5(a1,a2)-(b1,b2)…

Q: Let a = (2,3,6) and b = (3,4,2) be vectors.  Compute the cross product aXb

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Q: Suppose that u₁ and u₂ are orthogonal vectors, with ||u₁|| = 4 and ||u2|| = 2. Find ||5u₁ − u2||.…

A: The magnitude of the given vectors is:u1→=4u2→=2

Q: 7. Show that the vectors A=4a, -2a + 2a, and B = -6ā, +3ā, -3ā. e parallel to each are other.

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Q: Determine if the vectors , and are linearly independent.

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Q: Let a and b be vectors in R" such that ||a||=|| b||=2 and (a,b)= — . Then ||a - b||= ...

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Q: 1. Explain why the following form linearly dependent sets of vec- tors. (Solve this problem by…

A: According to our guidelines we can do only one question if multiple question are posted. Please post…

Q: Let the following vectors be in R³ a = (1,3,-1) b= (-2,1,3) c = (3,2,1) d = (1,-1,2) 15.- Find the…

A: Introduction: Vector Operations are operations that are performed on vector quantities. Vector…

Q: Find four different nonzero vectors that are orthogonal to v = (-1,5,2)

A: This is a simple problem based on orthogonal vector which could be solved by using basic knowledge…

Q: 5) Find a vector in component form that is orthogonal to the vectors a = (9,3,-7) and b = (10,-8,2)

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Q: What is the dimension of the vector space spanned by the vectors v1, v2? v1 = (6, -2, 4) and v2 =…

A: v1 = (6, -2, 4)  v2 = (14, 2,8)  There does not exist any real number c such that v1 = c v2 hence v1…

Q: Suppose ~u and ~w are vectors in R^n . Prove that if ~u and ~w are parallel vectors in the same…

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Q: ● Let A = (1.-2,4), B (0,3,2), C (-1,4,-2) be three points in R. Find the vectors u-AB and v-AC.

A: Let A=(1, -2,4), B=(0,3,2), C=(-1,4,-2) be three points in R3. We have to find the vectors u and v.

Q: 3.- Define the vector that allows the linear combination and if it exists, demonstrate the linear…

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Q: Find the norm of and the unit vector in the direction of if |||| = t = ↑ 2

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Q: Find a continuous solution satisfying dy dx + 2xy = f(x) where { x if 0 < x < 1 romer 0 if x ≥ 1 ,…

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Q: Let ~u = ( 1, -1, 0) and ~v = ( -1, 0, 1). Find ~u - ~v and ~u + ~v. b) Are the vectors ~u − ~v and…

A: Orthogonal vectors

Q: Prove that a(-3,2) and b (2,-3) form basis vectors in xy plane

A: a set is said to be basis if set is linearly independent and it spans the space.

Q: (a) Suppose that a and b are two unit vectors in R^3, and a·b=11/24. Find the norm of the vector 4a+…

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Q: 150. Determine the real number a such that vectors a = -3i+2j and b = 2i+aj are orthogonal.

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Q: Express the vector in the form (V= ai+ bj+ck) *, if A(1,0,3) and B is (-1,4,5):

A: Vector from

Q: Determine whether the set of vectors Q={(-1,1,1).(-1,0,2).(1,2,3)} spans R'.

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Q: Let V₁, V2, V3 be the vectors in R³ defined by 18 ---A V2 = -14 (a) Is (V1, V₂, V3} linearly…

A: We now solve this questions

Q: Let a and b be vectors in R" such that |la||=|b||= 2 and (a,b>=. Then ab..

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Q: Determine if the vector product = a0b0 defines a valid inner product on P2(R) for any…

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Q: 6. Show that the vectors (1,1,0), (1, 0, 1), and (0,1,1) generate F3.

A: In this question, we will show that the given vectors generate F3 .

Q: 9. Is the set of vectors {(-2, 2, 0), (1, 1, 1), (8, -4, 2)} over R linearly dependent or…

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