= Consider two bases B = {u₁, u₂} and B' = {V₁, V₂} for a certain vector space V. Assume that u₁ = 4v₁ + V2 and u2 = −6v₁ + V2. If w = ¤ 3u₁ + u2, what is [w]B?

Q: 8. Show that (a) i=- (b) j= (c) k= jxk i.jxk kxi i.jxk ixj i.jxk 9. Find the vector triple product…

A: (a)                                (b)                            (c)…

Q: ▶Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, v3)…

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Q: Let u, v, and w be vectors, and let a be a scalar. Prove the given property. (u + v) · w = u·w + v.…

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Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3 )…

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Q: Q12: Let vector v = (1, 3) and vector w=(-4,-2). Write vector v as the sum of two orthogonal…

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Q: 1. Find the vector component of the vector ū (-3, 6, 2). [28, 63, 0] in the direction of = %3D

A: We have to find vector component of u =[28, 63,0]  along the direction v=[-3, 6,2] Vector component…

Q: If A and B are both second-order tensors and t, u, v, and w are all vectors, prove the following…

A: Given that if A and B are both second-order tensors and t, u, v, and w are all vectors.   (1). To…

Q: To express the vector =(1.2 -6) as a linear combination of three vectors ,- (0.1. 2), v= (1,0.2) and…

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Q: Let ū = (4, –2), ū = (-2,0), and w = (2, 2). Find the vector x that satisfies Tu – u +x = 5x + w. In…

A: Given Let Plugging the values in the equation:

Q: Suppose V₁, V₂, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such…

A: The objective of the question is to verify if the vector w is equal to the sum of the vectors V1,…

Q: Q3) A) Let 4 (-1 3, 4) and B (-5, 8, 10) two points in the space, find: 1- The vector AB. 2- Length…

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Q: Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

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Q: Let W be the set of all vectors of the form ū = H V = [-5s- 2t] 5s + 3t 5s + t . Find vectors ū and…

A: Let S={u,v} be a linear independent set and generate W . Then W=span{u,v} .

Q: Let m = (-3,1,5) and n = (5,-1,2). calculate the vector p = n - ((m*n)/(m*m))*m.

A: here we get p=0

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: Let vv be the set of all vectors of the form -a b vectors u and in R³ such that W = span{u, v}. ū =…

A: Given space W =

Q: Find the vector z, given that u- (9, 2, 7), 2,-1), andw = 0,-4

A:

Q: What is the dimension of the vector space P°?

A: The dimension of Pn is n+1

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: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such…

A: Given three vectors which span w.

Q: (2) Let vị = ( 2 = (2),v3 1 of the vector space R³. (2a) Does the vector v = (6 belong to…

A: Linearly independent vectors: The set of vectors v1, v2, ..., vn is said to be linearly independent…

Q: Let u4 be a vector that is not a linear combination of {u₁, U₂, U3, }. Select the best statement. ©…

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Q: sider the ordered bases B= ((4, –9), (–3,7)) and C = ((4,3), (–2,4)) for the vector space R’ %3D

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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: Let u = u1i + u2j + u3k, v = v1i + v2j + v3k, and w = w1i + w2j + w3k be vectors in R3. Show that

A: given: u=u1i+u2j+u3kv=v1i+v2j+v3kw=w1i+w2j+w3k we have to show that: u×v.w=u1u2u3v1v2v3w1w2w3

Q: Let y = *₁ = 0 and ū= 6 . Write y as the sum of two orthogonal vectors, ₁ in Span{u} and 2…

A: Given that the vectors  y→=0-1-2   and  u→=56-1   .

Q: Express the vector x as a linear combination of the u's. -17 U₁ = 0, U₂ = 5, U3 = 6, X = -43 -14…

A: