Question

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)

Answer 1

[tex]\left[\begin{array}{cc}1&2\\4&1\end{array}\right] +2* \left[\begin{array}{ccc}0&x\\y&0\end{array}\right] = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right] [/tex]

$\left[\begin{array}{cc}1&2\\4&1\end{array}\right] + \left[\begin{array}{ccc}0&2x\\2y&0\end{array}\right] = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

$\left[\begin{array}{cc}1&2+2x\\4+2y&1\end{array}\right] = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

$2+2x=0 =\ \textgreater \ x=-1$
$4+2y=0=\ \textgreater \ y=-2$