Let T: P3 → R³ be defined by T(ao + a₁ + a₂x² + ³x³) , and C= (18-8-8) Given [7] Pc (T(u)). = 4 1 -4 0 -2a1 + a2-a3 -2a0-a₁ 3a2 + 3a3 -ao-3a2 + az Let u = 2x² + x³, B = {x³, x², x, 1] -2 0 1 -2 use the Fundamental Theorem of Matrix Representations to find 1 1

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Q: 7. Evaluate * (D5 - 3D4 + 8D³ + 16D² - 9D - 13)y = 0 y = (C₁ + C₂x)e¯x + С3ex +C4e²x cos3x + C5e²x…

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A: See the attachment

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Q: Let Var(X₁) = Var(X3) = 2, Var(X₂) = 3, Cov(X₁, X₂) = 2, Cov(X2, X3) -2, Cov(X1, X3) = -1. i)…

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Q: Integral Representation for F₁ : T(c) T (b) T (c − b) √ ¹³-¹ (1 − p)²-b-1 (1 − x1)¯ª di − 1⁰-¹ - 2…

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Q: Q1] (A) If F(x+y-z₁x² + y²)=0 where z = z(x, y) дz дz x -y =x-y ax (B) If f(x, t) = f²e-y²dy, then…

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A: To evaluate the given triple integral: ∫-10∫02∫01(x2+y2+z2) dz dy dx=∫-10∫02∫01(x2+y2+z2) dz dy…

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Q: Find all second-order three-step methods in the form Yn+1 = aoyn+q₂yn-l + a₂yn-2 +h[b_f (tn+1• Yn+1)…

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Q: Let T: P3 R³ be defined by T (αo + a₁x + a₂x² + a³x³) {0.00} 3 G and C = Given [7] Pc (T(u)). Pc…

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A: give r1(t)=9ti+2t2j+6t3k and r2(t)=t4k So  r'1(t) =9i+4tj+18t2k and r'2(t)=4t3k