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Porblemas sobre subespacios vectoriales?

Porblemas sobre subespacios vectoriales. Determine si W es un subespacio del espacio vectorial dado. 1) W = { (x, y, z) : x ≥ 0} V = R³ 2) W = { [tex] f [ / tex] : [tex] f [ / tex] ( - 1) = 0} V = C [ - 1, 1].

10Palechoez

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Definición de subespacio vectorial <img src="https://tex.z-dn.net/?

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Jorgemb1998

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Definición de subespacio vectorial <img src="https://tex.z-dn.net/?f=W%5Ctexttt%7B%20es%20un%20subespacio%20vectorial%20de%20%7DV%5Ctexttt%7B%20si%20%7DW%5Csubset%20V%5C%5C%20%5Ctexttt%7By%20adem%5C%27as%20se%20cumplen%3A%7D%5C%5C%20%5C%5C%0A1%29%20%5Ctexttt%7B%20Si%20%7Du%2Cv%5Cin%20W%5Ctexttt%7B%20entonces%20%7Du%2Bv%5Cin%20W%5C%5C%20%0A2%29%20%5Ctexttt%7B%20Si%20%7D%20u%5Cin%20W%5Ctexttt%7B%20y%20%7Dk%5Cin%20F%5Ctexttt%7B%20%20entonces%20%7Dku%5Cin%20W%5C%5C%20%5C%5C%0A%5Ctext%7BDonde%20%7DF%5Ctexttt%7B%20es%20un%20campo%20de%20escalares%7D" /> = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <img src="https://tex.z-dn.net/?f=1%29%20%5Ctext%7B%20Sean%20%7Du%2Cv%5Cin%20W%5Ctext%7B%20es%20decir%20%7Du%3D%28u_1%2Cu_2%2Cu_3%29%5C%2C%2C%5C%2C%20v%3D%28v_1%2Cv_2%2Cv_3%29%5C%5C%20%0A%5Ctext%7Bcon%20%7Du_1%5Cgeq%200%5C%2C%2C%5C%2C%20v_1%5Cgeq%200%5C%5C%20%20%5C%5C%0A%5Ctext%7BEntonces%20%7Du%2Bv%3D%28u_1%2Bv_1%2Cu_2%2Bv_2%2Cu_3%2Bv_3%29%5Ctext%7B%20note%20que%20%7Du_1%2Bv_1%5Cgeq%200%5C%5C%0A%5Ctext%7BPor%20ende%20%7Du%2Bv%5Cin%20W%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctext%7BPor%20otra%20parte%2C%20sea%20%7Dk%5Cin%20F%5Ctext%7B%20entonces%20%7Dku%3D%28ku_1%2Cku_2%2Cku_3%29%5C%5C%0A%5Ctext%7Bdonde%7D%2Cku_1%5Cgeq%200%5Ctext%7B%20de%20esto%20%7Dku%5Cin%20W%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctherefore%20W%20%5Ctext%7B%20es%20un%20subespacio%20de%20%7DV" /> <img src="https://tex.z-dn.net/?f=2%29%20%5Ctext%7B%20Sean%20%7Dg%2Ch%5Cin%20W.%5Ctext%7B%20Como%20es%20bien%20sabido%2C%20la%20suma%20de%20funciones%7D%5C%5C%0A%5Ctext%7Bcontinuas%20sobre%20alg%5C%27un%20conjunto%20%7DX%5Ctext%7B%20tambi%5C%27en%20es%20continua%7D%0A%5Ctext%7B%20en%20%7DX%5C%5C%5Ctext%7Bpor%20ello%20%7Dg%2Bh%5Cin%20C%5B-1%2C1%5D.%5C%5C%20%5Ctext%7B%20Note%20tambi%5C%27en%20que%7D%5C%5C%20%0A%28g%2Bh%29%28-1%29%3Dg%28-1%29%2Bh%28-1%29%3D0%2B0%3D0%20%5Ctext%7B%20por%20ello%20%7Dg%2Bh%5Cin%20W%5C%5C%20%5C%5C%20%0A%5Ctext%7BSi%20%7Dk%5Cin%20F%5Ctext%7B%20entonces%20%7Dkg%28-1%29%3Dk%5Ccdot%200%3D0%5C%2C%2C%5C%2C%5Cforall%20g%5Cin%20W%5Ctext%7B%20por%20fin%20%7DW%5Ctext%7B%20es%20subespacio%7D%5C%5C%5Ctext%7Bde%20%7DV" />.