Question

Va rog doar punctul c).

Answer 1

$\it X = \begin{pmatrix} a\ \ \ \ \ b \\ \\ c\ \ \ \ \ d \end{pmatrix} \Rightarrow X^t = \begin{pmatrix} a\ \ \ \ \ c \\ \\ b\ \ \ \ \ d \end{pmatrix} \Rightarrow -X^t = \begin{pmatrix} -a\ \ \ \ \ -c \\ \\ -b\ \ \ \ \ -d \end{pmatrix} \\ \\ \\ X= X^t \Rightarrow \begin{cases} \it a=-a \Rightarrow a = 0 \\ \\ \it d=-d \Rightarrow d = 0 \\ \\ c=-b \in \mathbb{R}\end{cases}$

$\it X\in {Q} \Rightarrow X = \begin{pmatrix} 0\ \ \ \ \ b \\ \\ -b\ \ \ \ \ 0 \end{pmatrix} \Rightarrow det(X) = b^2 \geq 0$