Show that if A is both diagomalizable and invertible, then so is A-1. Find a unit vector in the direction of the given vector:

Q: let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove that…

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Q: If u is a unit vector and a is a positive scalar satisfying au + = 0, find a and u.

A: If u is a vector and a is positive scalar satisfying   au+1,-2,5=0.  To find : a and u.

Q: Determine whether the following vectors are linearly independent in R3:

A: They will be linearly independent if  a(1, 1, 3) + b(0, 2, 1) = 0  results in trivial solution only…

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: Let v, w, and a be nonzero vectors such that v · a = w · a.Is it true that v = w? Either prove this…

A: Given: v, w and a is non zero vectors, such that: v·a=w·a To prove: v=w

Q: 21. With A as in Exercise 17, find a nonzero vector in Nul A and a nonzero vector in Col A.

A: Given matrix is A=6-4-32-969-6 The column space of A is the space generated by the column vectors of…

Q: Let u be a unit vector in Rn and let H = I − 2uuT . Show that H is both orthogonal and symmetric and…

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Q: Given the vectors ū = (-2, 1, 1) and V = (3, –1, 1), calculate the vector projection of ū onto V

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Q: Suppose that the vectors {v, u, w} are linearly independent in some vector space V. Prove that the…

A: Given that the vectors u, v, w are linearly independent in some vector space V. Then the linear…

Q: What are the components of vector a, given the following information

A: Components of a vector  :ax=|a|cosθay=|a|sinθNow Vectora→=ax,ay

Q: A. Find the values of a such that vectors and are orthogonal .

A: According to bartleby expert policy only one individual question is to be answered. Kindly repost…

Q: Show that, û . ûm = 0, Use only the fact that û,is a unit vector. Interpret this result.

A: Here we need to prove that dot product of a unit vector and its derivative is zero. Here we use the…

Q: Prove: If {u. ) and {W} span the same vector space, then u, are linearly dependent.

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Q: Let u and v be distinct vectors in a vector space V. Show that {u, v} is linearly dependent if and…

A: We have to show:Let u,v ∈ V , u ≠ v.{u,v}  is linearly dependent <=> u or v is multiple of…

Q: find II u II for the given exercise, and give a unit vector in the direction of u.

A: Now,

Q: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Determine the length of each vector.

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Q: Prove with a diagram the following: If e is a unit vector orthogonalto v, then e × (v × e) = (e × v)…

A: Cross product of 2 vectors A→ and B→ at angle θ is given by the expression A→×B→=|A→||B→|sinθ n^.…

Q: compute the vector v if the coordinate vector vS is given with respect to each ordered basis S for V

A: Given that, S=1-200,-1301,1000,0-110Also,vS=0102

Q: Find the vector projection of C = ⟨2, −6, −1⟩ onto D = ⟨3, 5, −4⟩ and hence write C as the sum of a…

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Q: A vector u for which || u || = 1 is called a(n)_______ vector.

A: u is a vector whose modulus is 1. u=1 For a vector, if the modulus or magnitude is 1 then the vector…

Q: Find the vector projection of B= 61+ij+2k onto A=1-2j-2k and scalar component of B in the direction…

A: projba = a.ba2b now, <a> = 6i→ + 3j→ + 2k→ <b> = (i→ -2j→-2k→) so, a.b = (6i→+3j→+2k→).…

Q: Consider the basis B of R consisting of vectors and 3 Find a in R? whose coordinate vector relative…

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Q: Find the scalar and vector projections of b onto a, where a=⟨−1,1,2⟩ and b=⟨−1,5,4⟩

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Q: Prove that if vector u is orthogonal to both vectors v and w, then u is orthogonal to v + w.

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Q: Determine whether the following vectors are linearly independent in R2:

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Q: . Find a basis for the space spanned by the given vectors v1, ….., V5. 2 3 1 10 3 3 9.

A: For the vector space Rn, a set of linearly independent vectors contain atmost n vectors. Also any…

Q: B

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Q: Define first the scalar product of a row vector a and a column vector b, each having the same number…

A: The given matrices are,

Q: Find the norm of x and the unit vector ü in the direction of x if ||| = u =

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Q: Show that the vector in B4 is orthogonal to the vectors in B1, and that the vector in B2 is…

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Q: Find a basis for the space spanned by the given vectors, v1,., v5.

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Q: Prove that a·a= = |a|2, where a is a vector with n components

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Q: . Prove that (only one): E - 4y-V3ay is a unit vector? a- F 2 b- A = 6ax - 3a, + 2a, and B = 3a, +…

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Q: Find the scalar and vector projections of b onto a, where a = (1, 2) and b = (-4, 1). 1. comp, b 2.…

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Q: Use Vector Set A (a1 and a2) with a vector from Vector B (b1, b2, or b3) to show that while this set…

A: Explained below

Q: If vector A is any non-zero vector, a unit vector in the same direction of A would be?

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Q: Find a basis for the space spanned by the given vectors, vl,., v5. [M]-3

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Q: Find the norm of v, and a unit vector that is oppositely directed to v. (a) v = (3, 3)

A: The given vector is v = 3, 3

Q: If Aj is a covariant tensor of the second order and Bi, Ci are contravariant vectors; prove that…

A: Given: Aij is a covariant tensor of 2ndorder To find: AijBiCj is an invariant tensor

Q: Show that if C is any two-dimensional vector then it can be written as a linear combination of the…

A: Given: C→ be any two dimensional vector spaceie.,   C→=x,y|x,y∈ℝFormula: Convex set∃ t,s∈ℝ such that…

Q: Find a basis for the space spanned by the given vectors, vl.,., v5. [M]

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Q: Let a = 2i and b = -2i + 3j be two-dimensional vectors. Compute la – b|.

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Q: . Prove: If a and b are both unit vectors, then axb is a unit vector only when a and b are…

A: since you have asked multiple questions in a single request, we would be answering only the first…

Q: For any vectorV and unit vector U parallel to V , then D-

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Q: Find the scalar and vector projections of b onto a. a = 3i - j+ 6k, b = j+

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Q: Linear algebra

A: From the given information:Let,

Q: Given an orthogonal basis B and a vector v, find the B-coordinate vector of v. V 8. b) B =

A: Let B=v1,v2,…,vn be a basis for a vector space V and v be any vector in V. The vector v can be…

Q: prove that 1 Ə div A; = {√g grk Ak} = div A¹, Əx* where A; and Ai are the covariant and…

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