The union of two subspaces of a vector space is not necessarily a subspace.

Q: Each of the given sets below is not a subspace because at least one of the 3 properties of being a…

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

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Q: Let v1=[ 1 0 −1 ], v2=[ 2 1

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Q: If V is the subspace spanned by (1,0,1) and (2,1,0), find a matrix A that has V as its row spence.…

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Q: Determine whether the set of all matrices of the form (:: ;). a bc 1o), where a+e 0, and b +d+f 0,…

A: Given: abcdef , a+c=0, b+d+f=0

Q: 4: Let H1 and H2 be two subspaces of R". Show that H1 n H2 is also a subspace of R".

A: To show a set W to be a subspace of the of a space X if a,b∈W then a+b∈W   and for a scaler λ and…

Q: Let L = {(2, −1, 6), (2, −4,3), (4, −13, 1)}. a) Show why I does not generate the full vector space…

A: This answer is given below.Explanation:

Q: What is the relationship between the kernel of a linear transformation from a finite dimensional…

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Q: The intersection of an arbitary collection of subspaces of a vector space is also a subspace.

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Q: Let V₁ 1 -2 3 2 {V1, V2,V3}. V₂ = 2 -2 V3 7 8 7 - 10 and u = Is u in the subspace of R4 generated by…

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Q: Find a linearly independent set of vectors that spans the same subspace of R as that spanned by the…

A: A collection of vectors spans a set if every vector in the set can be expressed as a linear…

Q: When you multiply a Hermitian matrix by a real number c, is cS still Hermitian? Show that iS is…

A: As per the question we have to prove that : If a Hermitian matrix S is multiplied by a real number…

Q: The shape's vector set is a subspace of R3

A: solution :-

Q: Show that the set            W={(a,b,c):a-3b+4c=0}  is a subspace of the 3-tuple space…

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Q: If we know that W is a subset of the vector space V and we know that W contains the zero vector 0,…

A: This statement is False.  By using property of subspace we can prove this statement is False.

Q: Let P₂ be the vector space of all polynomials of degree 2 or less, and let II be the subspace…

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Q: A base of the subspace W={ (a, b, c); a-2b+c=0} is:

A: According to the question,

Q: Show that the set T= {(a, b, c, d): 2a-3b+Sc-d=0} is a subspace of R'.

A: Given T=abcd∈ℝ4:2a-3b+5c-d=0 Let A be a 1×4 matrix defined by: A=2-35-1 Then the equation…

Q: Let M3,3 denote the vector space of all 3 × 3 matrices. Let L3,3 denote the set of all lower…

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Q: Determine whether W = {(a,2,b)la, b ER} is a subspace of R³.

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Q: Find the dimension of the subspace of all vectors in R5 whose first and third entries are equal. The…

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Q: Show that a subspace of a Hausdorff space is Hausdorff.

A: Prove that, a subspace of a Hausdorff space is Hausdorff.

Q: Is any subspace of a vector space convex? Justify your answer by giving a proof or a counterexample.

A: The objective of this question is to determine whether any subspace of a vector space is convex and…

Q: The intersection of any two subspace of a vector space is a subspace.

A: we have to prove that the intersection of any two subspace of a vector space is a subspace.

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

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Q: Show that if Z subspace of a space Y and Y is a subspace of a space X then Z is a subspace of a…

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Q: Determine whether the statement below is true or false. Justify the answer. A subset H of R" is a…

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Q: a+b+2c 2a +2b+4c+d :a,b,c, d e R b+c+d За + Зс + d

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Q: Is the union of two subspaces of a vector space, a subspace. Justify your answer.

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Q: Show that an arbitrary linear combination of two states Vs in the vector space V with the same…

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Q: Compute the projection of (1, 1, 1) onto the subspace generated by (0, 1, 0) and (-4, 1, 3)". Record…

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Q: Let V be an F-vector space and A, B, C are subspaces of V. (a) Show that the equation An (B+C) =…

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