f V(F) be a finite – dimensional vector space End W be a subspace of V, then W is finite limensional and dim. W ≤ dim. V. n particular, if W is a proper subspace of V, hen dim. W ≤ dim. V. Also V = Wif and nly if dim. V = dim. W.

Q: The set W : 3x - y = z -5w = 0} is a subspace of R*. What is the dimension of W Select one: а. 1 b.…

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Q: 8) Let u, v be non-zero vectors. Prove that (u, v) is linearly dependendent if and only the vectors…

A: Linearly dependent

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

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Q: Let W be the set of vectors in R* of the form ГЗа + 267 —а — b 3 a + c where a, b, c represent…

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Q: 12): x € R. Is W a subspace of V? Expalin your 3x- Q1. Let V = R³ and W = answer? Q2. Show that M2x2…

A: The properties of subspaces: Closed under multiplication; Closed under addition; Contains the…

Q: 3. Determine which of the following sets of functions are subspaces of F[a, b]. a) All functions f…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in 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: The linear operator L : R² R² given by L (²) 6x - a) (55x + y) = -1 Which of the following gives a…

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Q: False/True: If vectors V1, V2, ..., Un span the subspace V, then every vector in V can be written as…

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Q: Determine whether the given set S is a subspace of the vector space V. DA. V = C5 (I), and S is the…

A: A subset S of vector space V is said to be a subspace of V if it is closed under vector addition and…

Q: Let W be the subspace spanned by the u's. Write y as the sum of a vector in W and a vector…

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Q: The first four Laguerre polynomials are 1, 1- 1,2-4t +t2, and 6 18t + 9t2-1. Show that these…

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Q: Q6: Explain whether the following sets are not subspaces of R" for the appropriate value of n. a a a…

A: We have to show that given set are vector subspace or not

Q: HIf vectors x, y, z, u in the real vector space p (the polynomials) are defined by x(t)=1, y (t)=t,…

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Q: Let V be a vector space and W₁, W2 be subspaces of V. Then verify that W₁ + W₂ = {w₁ + W₂ : W₁ € W₁…

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Q: True or False, S is a subspace of R 3 x1 (8] x2 x3 S = O True O False 2x1 + x3 = 0, x1 + x2 = x3 = 0…

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Q: True/False: If V is a subspace of R", then dim(V) + dim(V+) = n. True False

A: This is true and follows from a famous theorem in linear algebra.

Q: Let W be the subspace spanned by u₁ and u2, and write y as the sum of a vector in W and a vector…

A: Let W be the Subspace Spanned by u1 and u2,Write y as the sum of a vector in W and a vector…

Q: 3. Is the set of all vectors (x, y) in R2 with the usual addition and scalar multiplication, a…

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Q: Be F1(x, x, x) e R³ and F2(a, b,0) e R³ a)show that F1 and F2 are subspaces of R3 b)show that R' =…

A: Solution of the problem as follows