22. Let the representation of L: R³ → R? with respect to the ordered bases S = (vị, V2, V3} and T {W1, W2} be 2 1 A 1 where --[ -- --E wi = []. VI = V2 = V3 = and W2 = (a) Compute [L(V1)]r, [L(v2)]7, and [L(v3)],· (b) Compute L(vj), L(v2), and L(v3). (c) Compute L

Q: 6. Suppose V is a complex vector space with dimension n and T E L(V) is invertible. Let p and q be…

A: In the question it is asked to prove p(0)q(z)=znp(1z).

Q: 4. Let T: R2 → R² be defined by T = {B.[4]). and B₁ = -x y X- ([])=[ + ][²] = {[1].8]} BVB RUE BUE…

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Q: For each of the examples below find an operator T* on a vector space space V such that for all x, y…

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Q: 6 -3 1 Let (u, v) be the inner product on R generated by A = -1 and let u = (4, 3), v= (-5,3). Find…

A: Given that   <u,v> be the inner product on ℝ2 generated by A=61-1-3. And    u=(4,3), v=(-5,3).…

Q: Let T be a linear operator on R³ such that the rational form of T is [T] B = 0-20 1 0 for some…

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Q: Let I = ff, (a2 – y?) dæ dy, where D = {(a, v) : 1< *y < 4,0 < a – y < 6, # 2 0, y 2 0} Show that…

A: Given: I=∫∫D x2-y2 dx dy where D=x,y:1≤xy≤4,0≤x-y≤6,x≥0,y≥0 .

Q: х — у — 2 T: R3 → R3 such that T Find bases for the range space and 2х + 3у + 2 За — 4у — 2х kernel…

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Q: (BH) Let L: P1 → P2 be defined by L(p(x)) = xp(x) + p(0). Consider the %3D ordered bases S = {x, 1},…

A: I used the definition of matrix of linear transformation to calculate the corresponding matrices

Q: 53. Consider the basis B of R² consisting of the vectors [3] [F]g = | 1 and We are told that i 93…

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Q: Let T: R² R² be defined by T Let u = T(u): ¹([^])=[^²=²] = X2 H | amnet C = { v₁ = [!] > v₂ = [2]}…

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Q: 2.4. Let V be a vector space and let v1, V2,..., Vn be a basis in V. For x = Ek=1 akVk, y = Prove…

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Q: Let V=R₂₂ [x] with (the inner product, 1 <f(x), g(x)) = f(x) g(x) dx Find a basis for the or…

A: Answer is not correct, since the second element is not orthogonal to x2+x+1. Please check and verify…

Q: For (a, B) E R?, define a function (-, -) : R² × R? → R by setting arr' + xy + Yx' + Byy' . 1. Find…

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Q: 3. Given the two ordered bases U, V below for R³ (also the standard basis E = [e1, €2, €3]) (): 1…

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Q: 7. Let V={(x,y) x,y € R}. Suppose addition and scalar multiplication are defined using the following…

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Q: Apply the Coram - Sahmidt or thomaratizatia trans form to given baris for R into an basis Uie the…

A: The given basis is B={(0,0,7),(0,1,1),(1,1,1)} We have to find the orthonormal basis of the given…

Q: Show that each of the following are not inner products on R³,

A: (a)We have to show that the function below is not an inner product on R3, where u = (u1, u2, u3) and…