Matematică
mamamama
2015-11-04 21:47:54
Puteti sa ma ajutati urgent la asta,va rog? Determinati nr reale x si y,stiind ca A+2B=I2,unde I2=(1 0 0 1) Matricea A=( 1 2 4 1) si B( 0 x y 0)
Răspunsuri la întrebare
mironel
2015-11-05 03:14:48

[latex]displaystyle A+2B=I_2 \ \ I_2= left(egin{array}{ccc}1&0\0&1\end{array} ight) \ \ A= left(egin{array}{ccc}1&2\4&1\end{array} ight)~~~~~~~~~~~~~~~~~B= left(egin{array}{ccc}0&x\y&0\end{array} ight) [/latex] [latex]displaystyle A+2B= left(egin{array}{ccc}1&2\4&1\end{array} ight) +2 cdot left(egin{array}{ccc}0&x\y&0\end{array} ight) =left(egin{array}{ccc}1&2\4&1\end{array} ight) +left(egin{array}{ccc}2 cdot 0&2 cdot x\2 cdot y&2 cdot 0\end{array} ight) = \ \ =left(egin{array}{ccc}1&2\4&1\end{array} ight) +left(egin{array}{ccc}0&2x\2y&0\end{array} ight) =left(egin{array}{ccc}1&2+2x\4+2y&1\end{array} ight) [/latex] [latex]displaystyle left(egin{array}{ccc}1&2+2x\4+2y&1\end{array} ight) =left(egin{array}{ccc}1&0\0&1\end{array} ight) \ \ 2+2x=0 Rightarrow 2x=0-2 Rightarrow 2x=-2 Rightarrow x=- frac{2}{2} Rightarrow oxed{x=-1} \ \ 4+2y=0 Rightarrow 2y=0-4 Rightarrow 2y=-4 Rightarrow y=- frac{4}{2} Rightarrow oxed{y=-2}[/latex]

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