(8) (a) Find a basis B3 of the plane 2x1 - 3x2 + 4x3 (2,3)T. - 0 such that (1, 2, 1)

Q: Which of the following sets of polynomials form a basis for P₂? (i) P₁ = 1 + 4x + 6x², P2 3+x = (ii)…

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Q: Let B= = (1, +2, (x - 1)², 42³) be an ordered basis for P3. Find the coordinate vector of f(x) = 1x³…

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Q: Find the coordinates of the vector (2, -3, 4, -5) relative to the basis (0, 1, 0, -1), (1, 0, -1,…

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Q: 3 = [2 +21 Verify Properties (vi) and (viii) in showing C²x2 is a 2+2i 4+i Let c₁= 21, C₂ = 1 + 2i,…

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Q: The vectors --[+]»-[i]»-[3]m² -]»-[3]»=[] V2 = span R2 but do not form a basis. Find two different…

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Q: Show linear dependence in part (ii) to show that ({1,0,1}) is a basis.

A: From part ii)We have to show that the set  is a basis of .We know thatA basis B of a vector space V…

Q: Find a basis of R3 that contains the vectors (1,0,1) and (1,-1,1)

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Q: (d) Show that the polynomials P₁ = 3 + 2x + x², P₂ = 2x+3x², p3= −2+x=2x² form a basis of the vector…

A: Using 1+2x-x^2=ap1+bp2+cp3 find a b c

Q: 10. (a) Define: Basis 6 -1 -2 2 3 -4 5 8 (c) Find dim(nul(B)) and dim(col(B)), does your result…

A: The given matrix B=-36-11-11-223-12-458-4. We have find a basis for the null space of B and the…

Q: Let S = {ax? + bx + a : a, b ɛ R}. Then a basis and the dimension of S are (a) basis: x2, x + 1;…

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Q: Say whether the polynomials P1 (x) = x³–7x²+4x, p2(x) = 3x³-x²+5x-1, p3(x) = x³+4x-x²+1 are linearly…

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Q: 3) Let C be a basis that contains vectors (1 + (-1) x + 1x² + 1x³), (1 + 2x + 2x² + (−1) x³), (1 +…

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Q: Find an orthonormal basis of the plane x₁ + 3x2 − x3 = 0.

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Q: Find the coordinate vector of p(x) in P., relative to the basis S= {p,.P.-P;}, where p(x) =…

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Q: hich of the following sets of polynomials form a basis for P2? 1, p2 1- 5х, рз || (i) p1 х, р4 (i)…

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Q: b) Find the value of k such that (-1,1,1), (1,1,1), (1, -1, k) form a basis of R²

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Q: Which of the following sets of polynomials form a basis for P2?

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Q: Show that B = {v1=(1,0,0), v2=(3,7,-2), v3=(0,4,1)} is a basis for R3

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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: b) Let v1 = (1,2,1), V2 = (2,9,0) and vV3 = (3,3,4). Show that S = (V1, V2, V3) is a basis for R³.…

A: Explained below...

Q: Oa + Ob+0c + 4d la + (-1) b+ (-2) c +4d Oa + 1b + (-2) c + 5d la + (-1) b+ (-2) c + 2d 2a + 1b+…

A: 1) Let Tabcd=0a+0b+0c+4d1a+(-1)b+(-2)c+4d0a+1b+(-2)c+5d1a+(-1)b+(-2)c+2d2a+1b+(-10)c+4d   To Find:…

Q: Represent the vector ⟨16,8,−14⟩ in terms of the ordered basis B={⟨5,−2,−2⟩,⟨1,−4,2⟩,⟨−1,−5,3⟩}.

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Q: Find an orthonormal basis of the plane x₁ +4x2x3 = 0.

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Q: T: P2 P₂ defined by T(a + bx + cx2) = a + b(x + 8) + b(x + 8)² Find the following images of the…

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Q: x-3x+1 7. Is the set {(1,2,-1,3), (1, -1, 2, 0), (-2, 0, 6, 6)} a basis for R¹? Justify your an-…

A: The objective of this question is to determine whether the given set of vectors forms a basis for…

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

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Q: . Find the coordinates of the vector v relative to the ordered basis B. a) B = {x² + 2x +2, 2x…

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Q: a) Find , \pl, d (p, q), and then find the angle between them for the polynomials in P2 if p(x)…

A: a) given polynomials belong to P2 , so their basis set will be {1,x,x2}  p(x)=-3x2+2x-5 =(-5,2,-3)…

Q: 3) Find a basis of F3 containing the vectors (1, 2, -3), (2, 6, -3)

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Q: One of the following vectors lies in span{ 2+ x + x2, 3+x- 2x2} (A) 2+ 2x + 7x? (B) 2 + 2x + 5x? (C)…

A: The linear span of the given vectors is of the form a(2+x+x2)+b(3+x-2x2)