4. Show/prove whether the following is a subspace. 1 {x € R3:x =| 3| +s 2+t1,for s,t e R}

Q: rove that W2 = {(a,b) E R² : a = 26²} is not a subspace of R?.

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Q: Let H = {[ 21 12 x1, x2 € R 1,2 Show whether or not H is a subspace of R3.

A: We satisfy the clouser and scaler multiplication and show that 0 vector is also in H so H is a…

Q: (1) Consider the space M2×2 (R) of 2 x 2 matrices equipped with the usual addition and scalar…

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Q: 1. Determine whether the set S is a subspace of V or not, where Explain your answer. S = {p(x) = P₁…

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Q: а. W- : x is a scalar |2x + y b. W = : x, y are scalars x + y c. W = +1 : x is a scalar

A: we have to check subspace.

Q: Please go through each option with explanation

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Q: a Let H = :a – 76 + 3c – d = 0}. First show that H is a subspace of M2×2. Then determine dim(H). d

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Q: Prove that W1 = {(a,b) E R² : 4a – b= 0} is a subspace of R2.

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Q: Prdlem 6.36 Pert B)

A: It is double Integral

Q: 4. Show/prove whether the following is a subspace. {x € R3:x =| 3 +s 2+t| 1 ,for s,t e R} 2

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Q: Recall that lines through the origin are subspaces of R². 2x and W₂ is the line y = If W₁ is the…

A: Given, W1 is the line y=2x and W2 is the line y=-3x ,we have to find which statements are true about…

Q: 2. Let V = E3 and W = {x|x = a(1,0,2) + b(1,-1,3)} and S = {x\x = (x1,x2, 1)} where a and b are any…

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Q: 1 = { x:= = < |x|<1} am an 1. Consider the set Y=[-1,1] as a subspace of R. Is A=< open set in Y? Is…

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Q: 5. Let U = {(u₁, U2, U3) E R³|u₁ + u2 - u3 = 0} and V = {(V1, V2, V3) E R³v₁ - 3v2 +5v3 = 0}. (a)…

A: (a)

Q: Prove that span (v1,v2,...,vn) is a valid subspace of R

A: We know that ,  spanv1 , v2 , .... , vn = a1v1 + a2v2 + ...... + anvn / a1 , a2 , ...... , an∈ℝ A…

Q: The set {(x,3): x is in R)} is a subspace of R2

A: The given set is x,3: x is in R. It is known that any subspace should contain identity element.

Q: 5. Let H = {x E R³| x1 + x2 + X3 = 0}. Prove that H is a subspace of R3.

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Q: Let X = {a, b, c, d} and TX = {ø, X, {b}, %3D {b,c}, {a,b,d}} be a topology on X. Let Y = {1, 2, 3,…

A: A function is continuous if and only if inverse image of every open set is open

Q: .: Remind that the set F of all functions from R to R is a vector space. Prove that the set E of…

A: We know that If W is a subset of a vector space V , then W is a subspace of V if and only if the…

Q: Which of the following sets are subspaces of R°? A. ((x, y, z) | x < y < z} B. ((x, y, z) | 5x – 9y…

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Q: 2. Let H be the set of all vectors of the form claim. 2t 0. Is H a subspace of R³? Show your

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Q: 2t 6. Let H be the set of all vectors Show that H is a subspace of R³. What is the -t dimension of…

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Q: 5. Let U = {(u1, U2, U3) E R3³|u₁ + u2u3 = 0} and V = {(v₁, V2, V3) E R³|v1 - 302 +503 = 0}. (a)…

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Q: how that if T is a linear operator on V and W1, W2 are T-invariant subspaces of V, en W1+ W2 is a…

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Q: Which of the following subsets of R* are subspaces of R*? b. W = {(a,b,c,d)| c=a+2b, d=a-3b}

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Q: Find the closest point to y in the subspace W spanned by V₁ and V₂ 2 4 -6 2 3 3 2 y = a. O O a O с…

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Q: Determine whether the subset of C(-0, co) is a subspace of C(-0, co) with the standard operations.…

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