Let T: P3 → R³ be defined by T (ao + a₁x + a₂x² + а3x³) {6.0·8} and C= 2 = 0 Given [7] Pc (T(u)). 4 Fx-5 = 1 ao - 3a2 + 2a3 3a2 + 2a3 2a0 +a₁ +3a2 – 2a3. 3a⁰-a1 Let u 2x² + x³, B = {x³, x², -3 0 1 0 -1 2 use the Fundamental Theorem of Matrix Representations to fin 6 2 -1

Q: assume that Pr[A′]=0.55, Pr[B]=0.35 , and Pr[A′∩B]=0.2. (1) Pr[A∩B]=Pr[A∩B]=   (2)…

A: Solution : Given information; P(A')=0.55 P(A)=1-P(A')=0.45P(B)=0.35 and P(A'∩B)=0.2

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Q: Let T: R³ R² be defined by T (C) X2 - [3²1-22] = -3x3 -3 7 -- {~ - [ ] - - [E] - - [ ]} -- ² - {~ -…

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Q: x1, x2, x3...... x20000 iid U(2, 9), find approximation for 2X-20

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Q: Evaluate the Cauchy principal value of 2 x 50% -dx 8 x 2 (x² + 1)²

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Q: Suppose z = x + iy and f(z) = z². Find a w = u + iv such that f(w) = i (A) u = √2, v=1/√2 (B) (C)…

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Q: 2) a) Let T: C² C²: Ty = [x+2y-iz] 2y + iz Lix+z-2z Find [7] B [7] B and P where

A: Given information  T  :  C2 →C2T xyz = x+2y-iz2y+izix+z-2z simplify it, T xyz = x+2y-iz2y+izix+z-2z…

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Q: 10. Subtract 2- V- 64x²y* from – 3– xy-9y' and express the result in a + bi form

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Q: Consider the following bijections on R: f (x) = - g(x) = x – 7 Then (f o g)¯'(x) =

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Q: F(d) F (c-d) T (c) where x 0 and c-d>0. -S₁₁²-¹ (1-1)-¹) ₂F₁1(a,b;d;xt) dt¸ 4-1 (1 - 2F₁(a,b;c: x)…

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