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.…

A:

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

A:

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)

A:

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

A:

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

A:

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

A: