Choose all that apply for the set S2 e R : 3x1 - x2+ 5x3 12 x3 O S2contains the zero vector. O Szis closed under scalar multiplication. O Szis closed under vector addition. O Szis a subspace of IR. None of the above.

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A: To determine whether the given subsets are subspaces

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Q: 3x3 Define T:R → R² by T 12 xi + 6x2 Find a non-zero vector in the kernel of T.

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Q: 3. This problem is about set addition and subspaces. Let di and d2 = span{di}, %3D 1 U = span{d2}.…

A: Sum of two subspace

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A: W=span

Q: Let x 4 || - N and y = Find the vector v = 3x - 4y and its additive inverse. 18 [2] 4

A: The additive inverse of a vector v = <a , b> is  - v = <-a , -b>

Q: If A is an n x n matrix and b + 0 in R", then consider the set of solutions to Ax = b. Select true…

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Q: Find a basis and state its dimension for the following subspace in Rª 3r+ 6s-t 6r-28-2t -9r+ 5s + 3t…

A: Given that 3r+6s-t6r-2s-2t-9r+5s+3t-3r+t: where r,s,t∈ℝ

Q: Let u be a linear combination of {1₁, 1₂, 13). Select the best statement. A. span{u₁, U₂, U3} =…

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Q: Which of the following sets is always linearly dependent? A set that contains the zero vector A set…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Determine whether the given set is a vector space with respect to the specified addition and scalar…

A: closure under adiition is clearly satisfied that is a+b=abalso commutative under addition…

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A: we will first find the equivalent matrix and then reduce it to row echelon form

Q: v1 Determine if the subset of R consisting of vectors of the form where v1 - v2+ v3 – v4 + v5- - Un…

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Q: 6. Show that the set of all 3 x 1 matrices is a vector space. **end**

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Q: Let v₁ = O 1 5, V₂ = No Yes -2 -7 13 and w= - 3 -6 19 Is w is in the subspace of R³ generated by v₁…

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Q: If V1 = [1 4 0] and V2 = [ -2 0 8], then determine all possible 1x3 row vectors V3 such that the set…

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