(1) Consider the space M2×2 (R) of 2 x 2 matrices equipped with the usual addition and scalar multiplication.

Q: 3. Determine whether the given set is a subspace of M2x2 with real entries. {6 ) la = b}.

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Q: 2. Let S be the subset of P₂ consisting of all polynomials of the form ax² + bx + c such that a + c…

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Q: (d) The set U = [Select] C : a, b, c, d e R, ab = cd is a subspace of R¹.

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Q: Suppose S consists of all points in R2 that are on the x-axis or the y-axis (or both). (S is called…

A: Given: The union of the two axes S consists of all points in R2 that are on the x-axis or the y-axis…

Q: Determine whether the set Wis a subspace of R4 with the standard operations. Justify your answer. a)…

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Q: Which of the following sets W is NOT a subspace of R3? (Select all that apply.) O w= y : 3x-y+2z-1=0…

A: To identify the which of the given sets are not subspace.

Q: Let X be a nonempty set with subsets, A, B, and C. Prove that A ∩ (B \ C) = (A ∩ B) \ (A ∩ B). I…

A: Given that X is a nonempty set with subsets, A, B, and C. The objective is to prove that…

Q: 20 n) Given below are subsets of different vector spaces. Determine whether or not each subset is a…

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Q: 2а + b - Зс 4а — 2b + 5с (а) S %— E R* : a, b, c ER a а +b+c a X1 X2 (b) S = ER: 2x + х2 — 7хз + 8х4…

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Q: Determine whether the subset W below is a subspace of R³ with the standard operations Justify your…

A: To check if the subset W is a subspace of R3 with the standard operation. W={(s, t, s + t)| s and t…

Q: The set of polynomials of degree exactly two is a subspace of P2.

A: False

Q: 5. If W is subspace, if A = : a. (A + B) is subspace these [8] € W and B = Non of above [8] € W,…

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Q: TRUE or FALSE: The subset W = {a+bX+cX²: a+b+c= 1} is a subspace of R₂[X]. FALSE TRUE

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Q: Explain why the subset а — b S = a +b а,bER -26 – 3a of R3 is or is not a subspace of R³.

A: Given subset of R3 is  S={a-ba+b-2b-3a|a,b∈R} explain if S is subspace of R3

Q: Function? x 2 468 -6+ SK LAILA O Yes ΟΝΟ Graph 4 -2 Function? K+ Graph 1 864 63 -24 -44 Yes O No…

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Q: For each of the following subsets of F3, determine whether it is a subspace of F³: (a) {(x₁, X₂, X3)…

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Q: pan(1,1 – x, 1 +x², 2x – 3) = span(2, 2 – x°, 2x² – x, x + 1). - %3D - -

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Q: Show {s,t,4s-3t)|s and t are in ℝ} is a subspace of ℝ3

A: Let A= {s,t,4s-3t)|s and t are in ℝ}To show A is vector space it is enough to show that   v1,v2…

Q: [{-----} x+y+z=-7 A. B. Which of the following sets are subspaces of R³ ? C. D. Z X Z +2=0} 7x -5x…

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Q: The following are sets in R². Assume these sets include the boundary lines. For each, give a…

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Q: Prove that the set W= { | a,b are real numbers } is not a vector subspace of R3.

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