rownanie z macierza transponowana

[kamiolka28]

Znajdz macierz X
\(\displaystyle{ X=X^{T} \cdot \left[\begin{array}{cc}-1&0\\6&-1\end{array}\right]}\) jak to ugyzc?;)

[janusz47]

\(\displaystyle{ X = \left[ \begin{array}{cc}a & b\\c & d \end{array} \right],}\)

\(\displaystyle{ \left[ \begin{array}{cc}a & b\\c & d \end{array} \right] =\left[ \begin{array}{cc}a & c\\b & d \end{array} \right]\cdot \left[ \begin{array}{cc}-1 & 0\\6 & -1 \end{array} \right] .}\)
Stąd:
\(\displaystyle{ a = -a + 6c,}\)
\(\displaystyle{ b = -c,}\)
\(\displaystyle{ c = -b + 6d}\)
\(\displaystyle{ d = -d.}\)

\(\displaystyle{ X = c\cdot \left[ \begin{array}{cc}3 & -1\\ 1 & 0 \end{array} \right], \ c\in R}\)