4. Let U=span{ū, , ū,, ū;} and U=span{û ,û, ûz} where ū,=(1,0,0,0), ū,=(0,1,1,0), ū,=(0,1,1,1) and u,=(1,0,0,1), u,=(1,1,0,0), u=(0,0,1,1). Determine the basis and dimension of U & Û.

Q: if x=u(1-v),y=(uv) then verify that a(u,v) a(x,y). =1 a(x,y)'a(u,v)

A: Given x=u1−v and y=uv We have to verify ∂u,v∂x,y⋅∂x,y∂u,v=1 Solve x=u1−v and y=uv for u and v, we…

Q: Let U=span u, ,ū2, ūz and Ü=span{ú, ,ú2,úz where ü,=(1,0,0,0), ủ,=(0,1,1,0), ủ,=(0,1,1,1) and…

A:

Q: Let U=span{uq ,U2,U3} Û=span {u, ,u,,u,} where ū,=(1,0,0,0), ū,=(0,1,1,0), ū,=(0,1,1,1) and…

A: (a) Given vectors are u1^→=1,0,0,1,u2^→=1,1,0,0,u3^→=0,0,1,1.   Consider U^=spanu1^→, u2^→, u3^→.…

Q: : let u = (1, 2, 3), v = (2, 2, -1) and w = (4, 0, -4) then u-v and v - u equal %3D None u - v =…

A:

Q: Let (V, (, )) be an inner product space and let f, g be vectors in V. if || f|| = 4, ||| 5 and || f…

A:

Q: If x, y and z are vectors in an inner product space such that (x, y) = (x, z), then y = 2.

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Let X = (1, 2, 3), Tx = (0, X, (1), (2, 3}}, then (X, Tx) is %3D %3D 1) a T1 space 2) a T2 space

A: T1 space: A topological space X has the T1 property if x and y are distinct points of X, there…

Q: Let F(x,y,z)=(−6xz2,6xyz,6xy3z)F(x,y,z)=(−6xz2,6xyz,6xy3z) be a vector field and…

A: Given, Fx, y, z=-6xz2, 6xyz, 6xy3zfx, y, z=x3y2z

Q: If V is the space of all vectors in R*that are orthogonal to W = Span{(1,0,2,1), (0,0,1,5)}, then…

A:

Q: If V is vector space, with u = (u, , U2) and v = (v, , v2) with u +v = (u,+v, , u2+v2) and ku =…

A: u=(u1,u2) , ku=(3u1,0) k=2, u=(-1,2)

Q: Prove that u, v, w ∈ R3     and [ u x v, v x w, w x u] = [ u, v, w]2

A:

Q: 26. Let u = (2,3,1), v = (1,3,0), and w = (2,23,3). Since (1\2)u- (2\3)v - (1\6)w = (0,0,0), can we…

A: It is given that u=2,3,1, v=1,3,0 and w=2,23,3. Also, 12u-23v-16w=0,0,0. To prove or disprove that…

Q: If G (x, y, z) = curlF (x, y, z), where - F(x, y, z) = (y — z, z — x, x - y), then div(curlG (x, y,…

A:

Q: 6. Let u = (1, 2, –3) and v = (4,0, –2). Compute u x v. 7. Let u = (2, 4, -4) and v = (1, –3, 1).…

A: Used vector cross product

Q: ôu ôu ôt ôx? u (0, 1) — и(1,1) - 0,1> 0, : 0 in (0,1) × (0,+∞), u(х,0) — и, (х),0 <x<1,

A: Given that the heat equation ∂u∂t-∂2u∂t2=0withu(0,t)=u(1,t)=0with ICu(x,0)=u0(x)

Q: Verify the Cauchy-Schwarz Inequality for u = (1, −1, 3) and v = (2, 0, −1).

A: u = (1, −1, 3) and v = (2, 0, −1) To verify the Cauchy-Schwartz Inequality for the given set of…

Q: if x=u(1-v),y=(uv) then verify that a(u,v) a(x,y)_1 a(x,y) a(u,v)

A:

Q: 1) The space (R²,O,O) is not a vector space where: (x, y) O (z, w) = (x + z + 1, y + w + 1) a O (x,…

A: A vector space is defined over field F that consists of a set on which two operations (addition and…

Q: Show that UE span{(1,2, – 1,0),(1,1,0,1),(0,0, – 1,1)} where u= (2,5, – 5,1) by finding scalars k,I…

A: We have,u=2,5,-5,1andu=k1,2,-1,0+l1,1,0,1+m0,0,-1,1---1

Q: Define spanning set. Determine whether the vectors u = (1,2,0), 2 = (-1,1,2) and uz = (3,0,–4) span…

A: We need to define spanning set and to determine if the given vectors span R3  This can be done as…

Q: Is the set X is linearly dependent or independent X = {(1,0,1,0), (0,3,0,1), (1,1,2,2), (3,4,1, −2)}

A:

Q: 1 W = 1 2- En -2 = Span{u, ū2, ¡3}, ü, = i, =.w = Spanfū, üz), : %3D Lo. 3 [1 1 [1] [0 1 [3]

A:

Q: If G (x, y, z) = curlF (x, y, z), where F (x, y, z) = (y – z, z – x, x – y), then div(curlG (x, y,…

A: given statement if false.

Q: Let v1 = (1,1,2) v2= (-1, 2, -2) v3= (-2,-1,1). Write u = (6,7,2) as a linear combination of v1 v2…

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Q: Find (u, v), ||ul|, |v||, and d(u, v) for the given inner product defined on RT. u = (1, 3, 0), v =…

A:

Q: Let U=span(ū, ,ū,,ū and Û=span {u, ,u,, where ü,=(1,0,0,0), ū,=(0,1,1,0), ủ,=(0,1,1,1) and…

A:

Q: Find (u, v), ||u|, ||v||, and d(u, v) for the given inner product defined on R". (0, 2, 1), = (2, 1,…

A:

Q: 26. Let u = (2,3,1), v = (1,3,0), and w = (2,23,3). Since (1\2)u – (2\3)v – (1\6)w = (0,0, 0), can…

A:

Q: Let F(x, y, 2) = (z, 1, y). a. Find divF and curlF.

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Q: Let R = {(0,1), (0,2), (1,1), (1,3), (2,2), (3,0)} Find R', the transitive closure of R

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Q: Find (a) u × v, (b) v × u, and (c) v × v. u = (−1, −1, 1), v = (−1, 1, −1)

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Q: Prove that u, v, and w are all in span(u, u + v, u + v + w).

A: To Determine: prove that u ,v and w are all in span (u,u+v,u+v+w). Given:  we have(u,u+v,u+v+w)…

Q: [2/3] |1/3, u2 |2/3 --2/3] 2/3 1/3 Let y 8 and W = Span{u1,U2}. (a) Let U = [u¡ u2]. Compute U"U and…

A:

Q: (b) A = (0, 1] in the finite-complement topology on R. (c) A= {a, c} in X = {a, b, c} with topology…

A: The interior of a subset S of a topological space X is the union of all subsets of S that are open…

Q: Let u = (0, – 4,0) and v = (0,2,0). Compute |uxv. Then sketch u, v, and uxv. |uxv| =D

A:

Q: 5. Let U=span{ū ,ū2,ū;} and Ü=span{u ,ú,úz where ū,=(1,0,0,0), ū,=(0,1,1,0), ū,=(0,1,1,1) and…

A:

Q: In writing v as a linear combination of u ,,u, &u, ( if possible) given: y = (3,0, – 6) , u,= (1, –…

A:

Q: Prove that u, v, w ∈ R3     and [ u x v, v x w, w x u] = [ u, v, w]2

A:

Q: Find w such that 2u + v u 3w = 0. (0, 2, 7, 5), v = (-8, 4, -3, 1) 1 -- (-) W = 3 -

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Q: If V is the space of all vectors in R*that are orthogonal to W = Span{(1,0,2,1),(0,0,1,5)}, then…

A:

Q: Let W (s, t) = F(u(s, t), v(s, t)) where W,(1,0) WŁ(1,0) = u(1,0) = -1, u,(1, 0) = −5, ut(1,0) = -7…

A:

Q: 49. Show that in the vector space V, (R), the vectors (1, 2, 3), (- 2, 1, 4), (- 1, – 1/2, 0) form a…

A: We prove that the set of vectors form a linearly dependent set.

Q: Let u=0,3,3 and v=32,3,3. Compute u×v. Then sketch u​, v​, and u×v.

A:

Q: If R = {(1, 2), (1, 4), (2, 3), (3, 1), (4, 2)}, what is the symmetric closure of R? %3D О (1, 2),…

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Q: Suppose {u,..., 4,, W1, ..., W,} is a linearly independent subset of V. Show that span (u;)…

A:

Q: 40. Let. u₁=(3, 1, 1), u₂ = (-1, 2, 1), and u3 = (-1/2,-2, 7/2). Verify {u₁, U2, U3} is an…

A: A set of vectors u1, u2, β3, ..., un is said to be orthogonal if ui·uj = 0 [ dot product ]  whenever…

Q: 38. Let u₁ = (2, 1, -1), u₂ = (3,-4, 2), and u3 = (2,7, a). Find all values of a such that {u₁, U2,…

A:

Q: If M¿(x, y, z) = R,(x, y, z) and Ry(x, y, z) = N¿(x, y, z), then F(x, y, z) (M(x, y, z), N(x, Y, z),…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 1 Exercise 5.1.4 Let u = V = 3 and w = Show that span {u,v, w} = span {u, v}. 5

A: NOTE: Refresh your page if you can't see any equations. .

Q: Find u. (v x w). (6, 6, 6) (1, 7, 0) - (0, 0, 1) > 3

A: Given that,u=6,6,6v=1,7,0w=0,0,1