let FC k be a Galois extension with Gal
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Q: Exercise (1-3): By Charpit method solve the following PDE (1): p²x+q'y=2
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Q: Romberg integration for approximating f(x) dx gives R2₁ = 3 and R₂2 = 3.12 f then f(1) =
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Q: 4. 2X e 2X dy + 2 (Ye - x) dx = 0 dy + dx Sinx + Cosxy = tanx
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- YShow that f (Z)= Z+ Con formal maps | 리/ = 1 ?. Let V, W be finite-dimensional inner product spaces and T E L(V, W). Prove: (a) If T is injective, then T*T is invertible and T† = (T*T)-!T*. (b) If T is surjective, then TT* is invertible and T† =T*(TT*)-!. 1b) Check whether or not if L/K and K/F are Galois extensions, then L/F is a Galois extension.
- let pooduct of direct and Droduct of G be a k. then direct zck). z'G) is ZCH) andDraw the spin field F = and vertical components at a representative assortment of points on the circle x² + y² = 9. First find the horizontal and vertical components of the vectors at the 3√2 3√2 3√2 3√2) 2 2y 2x 2 √2+3² j along with its horizontal +y² 1 representative points (3,0), (0,3), 3√2 3√2 3√/2 3√√2 1/2). respectively, where V₁ 2 2 2 corresponds to the first listed point, v₂ corresponds to the second listed point, and so on. (0, -3), and V₂ 2 2 II 1 1-31 (-3,0), 2 V₁ = V3 = V5 Vg V6 V7 = (Type ordered pairs. Type an exact answer for each coordinate, using radicals as needed.)Let f, g € P₂ (R) and define (ƒ,g) = f(0)g(0). Select all the conditions which (•, .) do not met, or else conclude that (·, ) is an inner product on P₂ (R). 2 Select all correct options. (f, g) = (g, f) for every f, g = P₂ (R) (f+g,h) = (f, h) + (g, h) for every f, g, h = P₂ (R) 2 (Xf,g) = X(f, g) for every f, g = P₂ (R) and λ E R (f, f) ≥ 0 for every f = P₂ (R) 2 (ƒ, ƒ) = 0 if and only if f is the zero polynomial. (.,.) is an inner product on P₂ (R)