LABORATORIO Punto Equilibrio

¿Qué ocurre ahí? ¿No hay suceso? Todo es inmensamente suceso a través de esta calma densa hasta los bordes que sin titubear clausuran un equilibrio formidable".

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¿Qué ocurre ahí? ¿No hay suceso? Todo es inmensamente suceso a través de esta calma densa hasta los bordes que sin titubear clausuran un equilibrio formidable".

¿Qué ocurre ahí? ¿No hay suceso? Todo es inmensamente suceso a través de esta calma densa hasta los bordes que sin titubear clausuran un equilibrio formidable".

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A non-empty subset W of a vector space V is a subspace of V if and only if it is closed under addition and scalar multiplication; that is, x 1 , x 2  W implies x 1 + x 2  W, and c  F, implies c x 1  W. Proof: Closure under scalar multiplication does the trick for us. For any x  W, we have 0 = 0 w  W and −x = (−1)x W, by the properties proved in the last section.É Theorem 1.2: Second subspace test: A non-empty subset W of the vector space V over F is a subspace if and only if, for any a, b  F and x, y  W, we have a x + b y  W. Proof: If W is a subspace, and a, b, x, y are given, then the closure laws show that a x + b y  W. Conversely, suppose that this condition holds. Then, choosing b = 0, we see that a x  W for all a  F and x  W; that is, W is closed under scalar multiplication. Similarly, choosing a = b = 1 shows that it is closed under additionÉ.