Question

Punctul c) ..va rog mult !

Answer 1

X ∈ M₂ ⇒ $\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]$

A · X = $\left[\begin{array}{ccc}1&1\\1&1\end{array}\right]$ · $\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]$ = $\left[\begin{array}{ccc}a+c&b+d\\a+c&b+d\end{array}\right]$

(A · X) · B = $\left[\begin{array}{ccc}a+c&b+d\\a+c&b+d\end{array}\right]$ · $\left[\begin{array}{ccc}1&-1\\1&-1\end{array}\right]$ = $\left[\begin{array}{ccc}a+c+b+d&-a-c-b-d\\a+c+b+d&-a-b-c-d\end{array}\right]$

Deci A · X · B = O₂ ⇒ $\left[\begin{array}{ccc}a+c+d+b&-a-b-c-d\\a+b+c+d&-a-b-c-d\end{array}\right]$ = $\left[\begin{array} {ccc}0&0\\0&0\end{array}\right]$ ⇒ suma elementelor din matricea X, adica a+b+c+d=0