Let ={t?-1, t²-t, -t?+t-2} be a basis for P,(R). Then the coordinates of p(t)=6t2-3t-1 are [p]= %3D

Q: Explain why S is not a basis for P2. S = {1, 4x, -6 + x², 7x} O sis linearly dependent. O s does not…

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Q: Let B = {1, x, x², x*} be an ordered basis for P3. Find the coordinate vector of f(x) = 4x3 – 72² +…

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Q: Explain why S is not a basis for P. S = {1, 8x, -4 +x², 9x} O sis linearly dependent. O s does not…

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Q: Let W = } t s,t e R -S - 31 5) Show that -6 is in W+. 3 6) Find a basis for W+.

A: given W=s+3tt-s-t  , s t ∈R

Q: Explain why S is not a basis for P2. S = {1 – x, 1 – x², -1 – 3x + 4x²} O is linearly dependent. O s…

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Q: Explain why S is not a basis for R². S = {(-6, 2)} OS is linearly dependent. S does not span R². OS…

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Q: Explain why S is not a basis for P2. S = {1, 4x, -9 + x², 7x} S is linearly dependent. O s does not…

A: Given S={1,4x,-9+x2,7x}. We explain why S is not a basis for P2.

Q: 14. The set B = {1 – t²,t – t², 2 – t + t²} is a basis for P2. Find the coordinate vector of p(t) =…

A: Given vector is: Pt=1+3t-6t2 Basis set for the vector is given as: B=1-t2, t-t2, 2-t+t2 Then, let…

Q: Let B = {1+t, t – t2, 2t + t2} be a basis for P2. Find [-3+t – t°]B. %3D

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Q: [M] Let H = Span {v1, v2, V3} and B = {v1, V2, V3}. Show that B is a basis forH and x is inH, and…

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Q: B- {-x+x², -x², l-x5 2 2 C=? 2+x -x?, 2-x?, 3+x=2x2} 1 2+ X a) Find the a). change of basis matrix…

A: Given that  B={-x+x2,-x2,1-x} and  C={2+x-x2,2-x2,3+x-2x2} We find the change of basis matrix…

Q: 2) Let T(a+bx+cx² + dx³) = i) A basis for Ker(T) would be: ii) The Nullity of T is: iii) The Rank of…

A: As per our guidelines only first Question is solved. To get solution of remaining question kindly…

Q: Explain why S is not a basis for P,. S = {1 - x, 1 – x?, -1 – 2x + 3x?} O sis linearly dependent. O…

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Q: Explain why S is not a basis for P2. S = {1 – x, 1 – x², –1 – 6x + 7x²} S is linearly dependent. O s…

A: Consider a matrix formed by vectors of S and determine the determinant of the matrix, 1-1010-1-1-67=…

Q: Y1 Y2 ER3 [Y3. (x, y) 2x1y1 + X2Y2+5x3Y3, for x = |X3 (a) Find a basis for the orthogonal complement…

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Q: Let B be the basis of P3 consisting of the Hermite polynomials 1, 2t, - 2 + 4t“, and - 12t + 8t°;…

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Q: {( a + b+c+d b – c+ 2d а + 2с — d H = : a, b, c, d e R } C R³, and consider --(}) u = 1 (а) Is u E…

A: Given, H=a+b+c+db-c+2da+2c-d: a,b,c,d∈ℝ⊆ℝ3      ⋯⋯(1) a) Given, u=111 Consider the system,…

Q: Find the matrix A' for T relative to the basis B'. T: R2 - R2, T(x, y) = (-8x + y, 8x – y), B' =…

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Q: 2. Let T: P2- P2 be defined by T(a+ bx + c?) = a - 2b+ (2b – 4c)x+3ca². Find a basis C for P2 such…

A: Given T:P2→P2 defined as…

Q: Let B = (1, x, x², x³) be an ordered basis for P3. Find the coordinate vector of f(x) = - 823 6x? –…

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Q: The vectors 11 v1 = -4 V3 4 -5 form a basis for R° if and only if k +

A: The vectors are basis of R3 if they are not linearly dependent.

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: 1. Find [p]a, relative to the basis 3 = {P1. P2: Ps} for P, where p = 4- 3x +x², P1 = 1, P2 = X, P3…

A: Given

Q: Explain why S is not a basis for P,. S = {1 – x, 1 – x², –1 – 6x + 7x²} O s is linearly dependent. O…

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Q: Explain why S is not a basis for M, 2: -{::}[::} 0 1 1 S = 0 1 1 0 S is linearly dependent. s does…

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Q: What is the coordinate vector for the polynomial p(x) = 2 – x² + x'relative to the standard basis…

A: our objective is to find the coordinate vector for the polynomial p(x).

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: Let P2 denote the vector space of all polynomials in the variable a of degree less than or equal to…

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Q: Explain why S is not a basis for R2. S = {(-6, 6)} O sis linearly dependent. S does not span R². S…

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Q: B = (f1, f2, f3) is a basis for R2[] where fi = 1+ 2x + a², f2 = 2+ 3r + 2x², f3 = 2 + x +3x². If…

A: The correct option is option (e) 1 + 2x²   The detailed solution is as follows below:

Q: Let B be the basis of P, consisting of the three Laguerre polynomials 1, 1-t, and 2-4t+t, and let…

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Q: . ) The set B = {4x² – 4, 4x – 20 + 20z², 37 – 8z - 36x²} is a basis for P. Find the coordinates of…

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Q: Let s = {(r² –3r+4, 2r-5, x²+1} be a basis for P2, let q E P2. If (q). = [2,-3, 1], then q = %3D %3D…

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Q: Find the coordinate vector of p(x) = 5 - 2x + 4x² with respect to the basis B = (1 + x, 1 – X, x?}…

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Q: Explain why S is not a basis for P2. S = {1, 6x, –7 + x², 8x} S is linearly dependent. O s does not…

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Q: Find

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Q: .2 The set B= {1 +t,-t-t,1+2t+t} is a basis for P,. Find the coordinate vector of p(t)= -3-5t-6t…

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Q: Explain why S is not a basis for P,. S = {1 – x, 1 – x², -1 – 6x + 7x²} O sis linearly dependent. O…

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Q: Explain why S is not a basis for P2. S = {1, 6x, –5 + x², 8x} O sis linearly dependent. S does not…

A: Basis: A non-empty subset B of a vector space is basis if a) B is linearly independent b) B spans V.…

Q: Explain why S is not a basis for P. S = {1, 2x, =7 + x², 9x} O S is linearly dependent.

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Q: Find a basis for the plane 4x + 3y + 5z = 0 in R³.

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Q: Let {f1, f2, f3} be the dual basis of {e1, €2, €3} for R³, where e₁ = (1, 1, 1), €₂=(1,1,−1), Find…

A: Given basis are e1,e2,e3 of R3 where e1=1,1,1e2=1,1,-1e3=1,-1,-1 Its dual basis are f1,f2,f3 We have…

Q: Explain why S is not a basis for P2. S = {1, 8x, -6 + x², 3x} O sis linearly dependent. O s does not…

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Q: Let B = (1, x + 2, (* – 1)", 9x) be an ordered basis for Pg. Find the coordinate vector of f(æ) = 8a…

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Q: B = (f1, f2; f3) is a basis for R2[r] where fi = 1+z+2r², f2 = 1+2r + 5x², f3 = 2+1+2r². If g e…

A: Coefficient of linear combination is given. We have to find the element

Q: Define T : P2 → R² via T(a + bx + cx²) = (a + b, b – c) . Find a basis for ker T. Also, find dim(ker…

A: The detailed solution is as follows below:

Q: Explain why S is not a basis for P,. S = {1 – x, 1 – x2, -1 – 7x + 8x²} O sis linearly dependent. O…

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Q: Explain why S is not a basis for P₂. S = {1, 6x, -2 + x²,4x} O S is linearly dependent. OS does not…

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Q: a b 1) Let T cla + 2b + 1c + 3d + (-11) e+ (-la+ (-1) b + (-2) c + Od + 7e) x. d to Then a basis for…

A: The given transformation is  Tabcde=1a+2b+1c+3d+-11e+-1a+-1b+-2c+0d+7ex To find a basis for KerT⊥.

Q: Let B be the basis of P, consisting of the three Laguerre polynomials 1, 1-t, and 2- 4t + t, and let…

A: Find your answer below