2. Determine if the set is a basis of R3 [t] . {t² + 2t -3, t² + 5t, 2t² — 4}

Q: The set B = {3+4x², 12 − 3x + 16x², 9x - 25 - 36x²} is a basis for P₂. Find the coordinates of p(x)…

A: Here we have to find the coordinates of p(x) relative to the basis B.

Q: The set - B = {−2+2x², −6+ 4x + 6x², − 6 + 8x + 8x²} is a basis for P3. Find the coordinates of p(x)…

A: Given basis is .Also given that we have to write down it as linear combination of basis elements,Now…

Q: Let M be the set of all vectors in the form  ...(see attached picture)  where a , b and c are…

A: Notice that…

Q: the basis of P2 cons tive to B.

A: Introduction: For some n, consider V to be a subspace of Rn. A basis for V is a collection of…

Q: Explain why S is not a basis for P2. S = {1 - x, 1 - x², -1 – 4x + 5x2} O sis linearly dependent. O…

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Q: The set B = {4+x², 20 - 3x+5x2, 45-6x + 11x2} is a basis for P2. Find the coordinates of p(x) = 6x -…

A: 30-1Explanation:

Q: The set B = • {1+t², −t+t², 1 + 2t+t²} is a basis for P₂. Find the coordinate vector of p(t) =…

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Q: Either use an appropriate theorem to show that the given set, W, is a vector space, or find a…

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Q: Find all subsets of the set S = {(1, 3, −2), (−4, 1, 1), (−2, 7, −3), (2, 1, 1)} that form a basis…

A: Consider the given set: Here the objective is to find all the subsets of a given set that form the…

Q: R* Basis ? Is t Ś (l,D,0,1),(0,1.0,0).(1,1,1.2).(0,1,1,1)3

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Q: f. If x₁ = (4,1,-1,1,0), then Ax₁ = g. If x₂ = (1, -2,-2,0, 1), then Ax₂ = Is X₁ in the null space…

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Q: 16. Determine whether the given set forms a basis for P3. {-1 -r', 2r + 2r", –2r + r – a*, 1+ r² +…

A: Follow the steps.

Q: Explain why S is not a basis for P2. S = {1 – x, 1 – x², –1 – 4x + 5x²} S is linearly dependent. S…

A: Given a set S={1-x, 1-x2, -1-4x+5x2}  To Explain why S is not a basis for P2.

Q: Consider the basis B3 = (x² - 1, x, 1) of P2 (R). Find [2x² + 3x − 5] B (2,3,-5) (2,3,-3) (3,2,-5)…

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Q: The set B = {3 − 3x², 15+ 4x − 15x², 48x² - (47+ 12x)} - - is a basis for P2. p(x) = 12x² [p(x)] B…

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Q: 4. Find a basis for the span of {[1, 2, 1]" , [3, 1, –1]", [1, –3, –3]"}

A: Given: uvw = 121, 31-1, 1-3-3 To find: The basis for the span. Concept Used: To find a basis for the…

Q: The set B={3-2x², 9+x-6x², 24x² - (34+ 3x)} is a basis for P₂. Find the coordinates of p(x) = 90x² -…

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Q: -10000- Show that the set spans R. Find a subset of these vectors that is a basis 3 2 3 for R3. 2.

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Q: The set B = {4- 2x², 12 + 3x − 6x², 18x² - (35 + 6x)} is a basis for P₂. Find the coordinates of…

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Q: Let V = span {1+ 2x – x² + 3r³, -2+x+x² – x*, -1+ 8r – x² + 7r", 3 + x – 2r² + r'}. Find a basis ß…

A: Step:-1 Note:- To span V we need the polynomials of degree 3, so dimension of V is 4. (think using…

Q: (a) Suppose that V =Span{ 2 2 8 Determine whether each of the following sets is a basis for V: 2 | 2…

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