53. Consider the basis B of R² consisting of the vectors [3] [F]g = | 1 and We are told that i 93 for a cer- 2 tain yector in R2. Find r.

Q: Consider two bases B= (b, b2) and C= (c, c2) for a vector space V such that b, =e, - 6cz and by =…

A: Given two bases  and  for a vector space V such that and . Also, given that and we have to find .…

Q: Suppose that u and v are two vectors with |u| = 1, |v| = 4 and u · v = −2. a. Compute |u + v|. b.…

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Q: 1. Compute the following for the vectors in R3, x [1 3 21T and y [40 1T y and y x (a) (b) 2 and y2…

A: From the given information, [1 3 –2]T and [4 0 –1]T.

Q: Consider the 4-vectors Aª = (a, 0, 2a, 0) and Bª = (23, 0, 0, 0), where a and 3 are non-zero real…

A: and .It is given that  is null vector.

Q: It is known that 0 is an eigenvalue with algebraic multiplicity 2 of the matrix A given below. Then…

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Q: Let j = | and ü .Write j as the sum of two orthogonal vectors, it -2. %3D an {u} and ¤2 orthogonal…

A: Given:- →y=-69  →u=5-2

Q: 3- The scalar component of the vector F in the direction of K is (K.F А- .K, В- K C-

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Q: Find Q for the QR factorization of A = = Ex: 1.23 3 -A V1 = 0 , V₂ = 3 10 -9 -3 0 0 10 1 -10 0.21 ,…

A: Given:Also the orthogonal vectors are  We have to find Q for the QR factorisation of given matrix A…

Q: Suppose that f is a vector of length 8 with F1{feven} = -2 – i and F{f»dd} = 3+i. %3D Compute the…

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Q: 5. Find the real part of the dot product of the vectors u" = (1 – i,1+ i) v° = (5+ i, –3 – i)

A: SOLUTION:

Q: . If u and v are nonzero vectors in Rº, why do the equa- tions u · (u x v) = 0 and v · (u x v) = 0…

A: The dot product of orthogonal vectors is equal to zero.

Q: 1. Find the vector ? directed from (2, −4, 1) to (0, −2, 0) in Cartesian coordinates and find…

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Q: 4. In R² a) Draw the grid corresponding to the basis 3 = 3.72] b) A certain vector v in R² has…

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Q: Given K= (-2,-1), L=(2,4), M= (-3,-1) and N= (1,4), Prove that KĽ and MN are equivalent by Showing…

A: Two vectors are Equivalent if they have same magnitude and direction.

Q: Given ri = 3i - ej +In2 k, r2 = 5i + 7 e'j - 4 k and r3= 7i-7j+ k. Find the unit vector of (a)…

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Q: 5. If we have two vectors (V₁ and V₂), V₁ is a vector perpendic through the points A(1, 2, 5),…

A: Introduction: When a vector is along the direction in another vector, the two vectors are parallel…

Q: 8-b. Find the real part of the length of the vector v° = (5 + i, –2 + 2i, –1+i)

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Q: Let A: = -7 2 6 -4 -1 - 9 6 5 7 5-8 3 Find a nonzero vector v in Col(A).

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Q: Find the Wronskian of the following vector functions: u(t)= 5t-4 -t · -| V v (t) = -t+4 5t

A: Let  ϕ1(t)  and ϕ2(t)  are two vector valued function  Wronskian of these  vector functions is…

Q: Which of the following sets of vectors is a basis for R?? {[:]}. 2 3.

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Q: The vector F = -ar + 2a expressed in RCS and in terms of is O None of the choices O - = (−cos0sind…

A: We can solve this using spherical co-ordinate matrix

Q: A Determine whether each of the following vectors is in W Let W be the set of all vectors Select an…

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Q: Using index notation, prove the following identities among vectors A, B, C, and D: (a) (A x B). (B ×…

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Q: 2n bị 2n 2n paz x a, , b2 = a, xa x a, , bz = a, x -аз ха,,

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Q: 7 Let a and b be vectors in R" such that ||a||=||b||=2 and (a,b) = 1. Then ||ab||= ...

A: Let a and b be vectors in ℝn such that  a=b=2 and <a,b>=72 . Then we have to find the value of…