Show that the given set V is closed under addition and multiplication by scalars and is therefore a subspace of R³. X -E Z V is the set of all Let a = a+b= X y 0 y such that z=0. and b = u 0 be two vectors in V. Find their sum a + b. (Simplify your answer.)

Q: Find a vector b such that |b| = 1/2 that is parallel to a = but with opposite direction.

A: Given that: |b|=12a=<-6, 3, -2>

Q: Find the dot product of the following vectors →uu→ and →vv→.. Refer to image below →uu→ ⋅⋅…

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Q: Find all values of h so that the set of vectors 4 forms a basis for R3? Justify your answer.

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Q: Let A and B be vectors in R. Show that ||A|| = || B|| if and only if A+ B is orthogonal to Ã- B.

A: To solve the given orthogonality problem related to vector.

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

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Q: S= {(3, 4), (-1, 1), (4, 0)} 0) = X ress the vector s₁ in the set as a linear combination of the…

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Q: let A = [1 5 -4 -3 0] and w = [1]            [0 1 -2  1  0]              [2]            [0 0  0   0…

A: Answer is in below steps.

Q: Find all values of b for which the vectors are orthogonal 〈b, 3, 2〉,〈1, b, 1〉

A: Concept - If two vectors say u and v are orthogonal, then their dot product is equals to zero.That…

Q: Consider the following vectors: -3 6 = | b2 || b3 where b1, b2 and b3 are any real numbers. Show…

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Q: Consider the set V of all real triples of the form (a, b, c) where c = a - 2b under the usual vector…

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Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

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Q: Given the set R² with the vector addition operation defined by (x₁₂1₁) (x₂, 1/₂) = (x₂+x₂₂3₁ +3₂ −2)…

A: Given a vector addition operation, we want to find the zero vector for the set .

Q: Determine whether the vectors u = (-3,9,6) and v = parallel, (4, –12, –8) are orthogonal, or…

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Q: -0-0--0--0--0- 1 19. Let S be a set of vectors such that u = whether the set of vectors is linearly…

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Q: 2. Each set below is a subset of R2. For each set, do the following: • Sketch a picture of the set.…

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Q: Consider the points C(3,-2,0), D(-1,5,-1). Let b be the vector with representation CD. Write b in…

A: Ans:

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

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Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: First we will express vector s1 a linear combination of other vectors s2 and s3soing so will give us…

Q: Which of these operators produces a scalar when it acts on a vector? A B D Ⓡ u. V V D2 V. Vx

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Q: Please solve this question with a good explanation. It is Linear Algebra question.

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Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: Given : s = {(1,2,3,4), (1,0,1,2), (3,8,11,14)}

Q: {{: ]-- The set P = b = c = a + d } is a vector space under usual addition and multiplication. Find…

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Q: Let u = [1, -6, 3] and v= [-3, 3, 0]T. Find the vector w = 3u - 2v and its additive inverse. W= W=…

A: The given vectors and .We have to find the vectors and find its inverse.

Q: Suppose {V1, V2, V3} are linearly independent vectors in a vector space V. Find the number(s) k such…

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Q: Prove that |A|B + |B|A is orthogonal to |A|B – |B|A, for any vectors A and B.

A: We need to show that |A|B + |B|A is orthogonal to |A|B – |B|A, for any vectors A and B. Here, |A|…

Q: Let x = V = -5 = -5 and y = Find the vector v = 5x - 3y and its additive inverse. 1.81 (18) 6 [:] 5

A: The given vectors  and .To find the vector  and its additive inverse.

Q: Find a representation of the vector AB = (4, -14) in R2 by giving appropriate values for the points…

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