Advanced Math Archive: Questions from June 27, 2023
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Determine that the vectors (1,1,1), (1,1,0) and (0,1,-1) are
linearly independent in (R3, +, R..) And in (C3, +, C..)
Ejercicio 2: Determinar que los vectores \( (1,1,1),(1,1,0) \) y \( (0,1,-1) \) son linealmente independientes en \( \left(R^{3},+, R ..\right) Y \) en \( \left(C^{3},+, C ..\right) \)
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- The eigenvalue problem y" + Xy = 0, y′ (0) = 0, y′ ( 3 ) = 2
solution: a) y = cos (2nx), λ = 4n², n = 1, 2, 3... b) y = sin
(2nx), λ = 2n, n = 1, 2, 3. . . Oc) y = sin (2nx), λ = 4n², n = 1
The eigenvalue problem \( y^{\prime \prime}+\lambda y=0, y^{\prime}(0)=0, y^{\prime}\left(\frac{\pi}{2}\right)=0 \) has the solution: a) \( y=\cos (2 n x), \lambda=4 n^{2}, n=1,2,3 \ldots \) b) \( y=\
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Encuentra el volumen del paralelepípedo con los vértices dados.
(0, 0, 0), (0, 4, 0), (−3, 0, 0), (−1, 1, 5), (−3, 4, 0), (−1, 5, 5
), (−4, 1, 5), (−4, 5, 5) Muestra la solución.
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