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Laur
Pe: 2013-02-07T12:55:46+02:00 In: In:

Matrici

1.Fie A apartine M_2(Z) astfel incat:

A^2-A=(6…….0)
(10……6)

Sa se determine ca A este inversabila si sa se determine inversa acesteia.

2.Sa se rezolve ecuatiile matriceale:

(3….-4…..2) (1)
(-2….3….-1)X=(0)
(1…..-1….-2) (-2)

Multumesc!

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3 raspunsuri

  1. PallMall

        \[ \begin{array}{l} \left( {\begin{array} 3 & { - 4} & 2 \\ { - 2} & 3 & { - 1} \\ 1 & { - 1} & { - 2} \\ \end{array}} \right)X = \left( {\begin{array} 1 \\ 0 \\ { - 2} \\ \end{array}} \right) \\ X = \left( {\begin{array} 3 & { - 4} & 2 \\ { - 2} & 3 & { - 1} \\ 1 & { - 1} & { - 2} \\ \end{array}} \right)^{ - 1} \left( {\begin{array} 1 \\ 0 \\ { - 2} \\ \end{array}} \right),Fie\left( {\begin{array} 3 & { - 4} & 2 \\ { - 2} & 3 & { - 1} \\ 1 & { - 1} & { - 2} \\ \end{array}} \right) = A \\ \det A = \left| {\begin{array} 3 & { - 4} & 2 \\ { - 2} & 3 & { - 1} \\ 1 & { - 1} & { - 2} \\ \end{array}} \right| = - 18 + 4 + 4 - 6 - 3 + 16 = - 3 \\ A^T = \left( {\begin{array} 3 & { - 2} & 1 \\ { - 4} & 3 & { - 1} \\ 2 & { - 1} & { - 2} \\ \end{array}} \right) \Rightarrow A^* = \left( {\begin{array}) { - 7} & { - 10} & { - 2} \\ { - 5} & { - 8} & { - 1} \\ { - 1} & { - 1} & 1 \\ \end{array}} \right) \\ A^{ - 1} = \frac{1}{{\det A}}*A^* = - \frac{1}{3}\left( {\begin{array}) { - 7} & { - 10} & { - 2} \\ { - 5} & { - 8} & { - 1} \\ { - 1} & { - 1} & 1 \\ \end{array}} \right) \Downarrow \\ X = - \frac{1}{3}\left( {\begin{array}) { - 7} & { - 10} & { - 2} \\ { - 5} & { - 8} & { - 1} \\ { - 1} & { - 1} & 1 \\ \end{array}} \right)\left( {\begin{array} 1 \\ 0 \\ { - 2} \\ \end{array}} \right) = - \frac{1}{3}\left( {\begin{array}) { - 3} \\ { - 3} \\ { - 3} \\ \end{array}} \right) \\ \Rightarrow X = \left( {\begin{array} 1 \\ 1 \\ 1 \\ \end{array}} \right) \\ \Pr oba \Rightarrow \left( {\begin{array} 3 & { - 4} & 2 \\ { - 2} & 3 & { - 1} \\ 1 & { - 1} & { - 2} \\ \end{array}} \right)\left( {\begin{array} 1 \\ 1 \\ 1 \\ \end{array}} \right) = \left( {\begin{array} 1 \\ 0 \\ { - 2} \\ \end{array}} \right)(adev) \\ \end{array} \]

    scuze de parantezele din unele matrice dar ma cam bate editorul de ecuatii

  2. Laur

    Multumesc foarte mult!

  4. DD
    profesor

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