Operatii cu matrice

therul3r Lun Noi 05, 2012 2:08 am

Am o si eu 2 exercitii cu matrice pe care nu inteleg cum se fac.

1)Se se determine matricea A,stiind ca : $4A+\begin{pmatrix} 1 & 2 \\ 5 & -3 \end{pmatrix}$ = $\begin{pmatrix} 5 &6 \\ -7& 9 \end{pmatrix}$

2)Sa se determine matricele A si B daca: $2A+B=\begin{pmatrix} 1 &0 \\ -1 &3 \end{pmatrix}$

Multumesc mult !

**Admin** Mar Noi 06, 2012 7:39 pm

Problema 1) Consideram matricea:
$\begin{array}{l} A = \left( {\begin{array}{*{20}{c}} a&b\\ c&d \end{array}} \right) \Rightarrow 4A + \left( {\begin{array}{*{20}{c}} 1&2\\ 5&{ - 3} \end{array}} \right) = 4\left( {\begin{array}{*{20}{c}} a&b\\ c&d \end{array}} \right) + \left( {\begin{array}{*{20}{c}} 1&2\\ 5&{ - 3} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {4a}&{4b}\\ {4c}&{4d} \end{array}} \right) + \left( {\begin{array}{*{20}{c}} 1&2\\ 5&{ - 3} \end{array}} \right)\\ = \left( {\begin{array}{*{20}{c}} {4a + 1}&{4b + 2}\\ {4c + 5}&{4d - 3} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 5&6\\ { - 7}&9 \end{array}} \right) \Rightarrow \left\{ \begin{array}{l} 4a + 1 = 5\\ 4b + 2 = 6\\ 4c + 5 = - 7\\ 4d - 3 = 9 \end{array} \right. \end{array}$
Rezolvând acele ecuații se obține a,b,c,d..... în concluzie matricea A.
b) la fel.

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