Question

Determinați matricea X€m indice2(R),știind ca X+A=2B
A(1 -2) B( 1 2)
1 3 -1 -2

Answer 1

$X \: \in \: M_{2}(\mathbb{R})$

$A=\begin{pmatrix} 1 & - 2 \\ 1 & 3 \end{pmatrix}$

$B=\begin{pmatrix} 1 &2 \\ - 1 & - 2 \end{pmatrix}$

$X + A=2B$

$X + \begin{pmatrix} 1 & - 2 \\ 1 & 3 \end{pmatrix} =2\begin{pmatrix} 1 &2 \\ - 1 & - 2 \end{pmatrix}$

$X + \begin{pmatrix} 1 & - 2 \\ 1 & 3 \end{pmatrix} =\begin{pmatrix} 2 \times 1 &2 \times 2 \\ 2 \times ( - 1) & 2 \times ( - 2)\end{pmatrix}$

$X+\begin{pmatrix} 1 & - 2 \\ 1 & 3 \end{pmatrix} = \begin{pmatrix} 2 &4 \\ - 2 & - 4 \end{pmatrix}$

$X = \begin{pmatrix} 2 & 4\\ - 2& - 4 \end{pmatrix} - \begin{pmatrix} 1 & - 2 \\ 1 & 3 \end{pmatrix}$

$X = \begin{pmatrix} 2 - 1 &4 - ( - 2) \\ - 2 - 1 & - 4 - 3 \end{pmatrix}$

$X = \begin{pmatrix} 1 &6 \\ - 3 & - 7 \end{pmatrix}$