Fyllad_ProkHL03 - FULLADIO 0 - Gr. 'Algebra Prokatarktikì....

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FULLADIO 0 - Gr. 'Algebra Prokatarktikì. HMMHU 2002-03 1. (a) Na apodeiqjoÔn oi idiìthtec: ( i ) ( AB ) > = B > A > , ( ii ) ( AB ) ? = B ? A ? (1) (b) Na apodeiqjeÐ ìti an oi pÐnakec B kai Γ eÐnai summetrikoÐ tìte gia opoiond pote pÐnaka A , oi pÐnakec A > BA kai A Γ A > eÐnai summetrikoÐ. (g) Na deiqjeÐ ìti gia kˆje tetragwnikì pÐnaka A isqÔei ( A ν ) > = ( A > ) ν , ν N . (d) Na apodeiqjeÐ ìti an o pÐnakac A eÐnai antisummetrikìc tìte o pÐnakac A ν eÐnai summe- trikìc an o ν eÐnai ˆrtioc kai antisummetrikìc an o ν eÐnai perittìc. 2. Na upologisjoÔn oi pÐnakec AB kai BA , ìtan A = 2 + i 4 + 3 i i 7 6 + 9 i 1 - i , B = 8 - 4 i 5 i 6 - 2 i 3 + 2 i 4 + 5 i . 3. Na upologistoÔn me qr sh idiot twn oi orÐzousec D 1 = α β γ δ - α β γ δ - α - β γ δ α β γ - δ kai D 2 = λ + α α α β λ + β β γ γ λ + γ . 4. Na lujoÔn oi exis¸seic (me metablht  x ) λ λ 2 x λ 2 x λ x λ λ 2 = 0 kai
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