Suppose {u, } form an orthogonal basis in R2 and y = 2ū - 7 where u = (8) 6 If W = Span{}, what is the distance between y and W?

Q: If the matrix of change of basis form the basis B to the basis B' is A= change of basis from B to B…

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Q: (a) Consider the real linear map T : R' - R', expressed as follows: (1 2 -1 49 -1 X1 X1 + 2x2 - x3…

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Q: Consider the vectors u= (-1, 2, 1) and v= (3, -1, 5).  (please solve last 3 letter) a) Show that u…

A: Introduction: Two vectors are perpendicular when their dot product equals to 0. Given: u= (-1, 2,…

Q: Show that {₁, ₂} or {₁, ₂, 3) is an orthogonal basis for R² or R³. Find the coordinate of with…

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Q: 7. Find any two ON (orthonormal) vectors in (a) span {(1,2), (6, -1)} (b) span {(1, 2, 4), (2,…

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Q: Compute the orthogonal projection of v = proj, (v) = -5 onto the line L through -4 and the origin. 6…

A: Introduction:  The vector projection of a vector a on (or onto) a nonzero vector b, sometimes…

Q: Let a = (-4, 3, 4) and b = (-5, 2, 3), then find the decomposition a = a +a of a with respect to b a…

A: Ggg

Q: Prove that the vectors (a1, a2), (B₁, B₂) = R× Rare linearly dependent iff α₁ß2 - α2ß₁ = 0.

A: The given vectors are  and We have to show that the given vector is linearly dependent if

Q: A vector v in a plane is a line segment with a specified direction, where the component form is…

A: Part(a) Given vector

Q: y Suppose E (A, B) is controllable. Suppose a change of basis is performed so that we obtain a new…

A: As per the question we are given a controllable system as : ∑ ➞ (A, B) And after a change of…

Q: Which matrix could be used to rotate a vector 64 degrees clockwise about the origin? cos (-64) sin…

A: we have to find  matrix could be used to rotate a vector 64 degrees clockwise about the origin.

Q: Are the vector spaces R4, M2,2, and M1,4 exactly the same? Describe their similarities and…

A: We have to determine if the vector spaces, are exactly the same or there is any similarity or…

Q: Triangle ABC is formed by three lines: (;)-(9) +-(;) - (AB) is 3 +r (AC) is and 6 -2 2 1 (;) - (")…

A: We are only allowed to solve one question at a time and up to three sub-parts. Please post the…

Q: 8. Let 1 2 +--+- () -- () ---(3) (:). at = and = 3 4 7 b3 (a) Find conditions on b₁,b2, b3 such that…

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Q: (1) Let B = {√₁, 72, 73} be the basis of R³ defined by 1 *-(). *- (). *-(1) ), = = = Find the dual…

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Q: If u and v are vectors in R^n, and if v≠0 ⃗, then u can be expressed in exactly one way in the form…

A: first draw a figure as below

Q: Show that the vectors (1, 1, 2), (1,2,5), (5,3,4) of R'(R do not form a basis of R'(R).

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Q: Find the vector in component form with initial poi

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Q: Which vector in two-dimensional space has no corresponding unit vector?

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Q: need help on this question   given the basis B={[12],[25]} of R2.{"version":"1.1","math":"\mbox…

A: We have to find the change of coordinates matrix from the standard basisE=1,0,0,1 of ℝ2 to the basis…

Q: (a) Find the vector projection of a onto b , that is, find proj, a . (b) Find a vector in the…

A: We can solve the problem problem using concept of vector.

Q: 4) Let V = M2x2 (C) with standard basis B = (m₁, m2, m3, m4) and let T : V → (a) (b) (c) T((& $)) =…

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Q: Suppose that u, v, w are vectors in R^36 such that u. u = 3 u. V = 0 u.w=0 V.V=9 if x is a vector in…

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Q: Consider an inner product on two P3 vectors as (f, g) = f(-1)g(-1) + f(0)g(0) + f(1)g(1) + f(2)g(2):…

A: Since you have posted multiple subpart question, we will solve the first three sub parts for you. If…

Q: (-9,6) Use matrices to reflect the vector the line y = x. ove

A: Topic:- algebra