Oblicz równanie macierzowe:[tex]\left[\begin{array}{cc}-1&5\\2&0\end{array}\right] * X = \left[\begin{array}{c}2&-4\end{array}\right][/tex]

Odpowiedź :

[tex]\left[\begin{array}{cc}-1&5\\2&0\end{array}\right]*X=\left[\begin{array}{c}2\\-4\end{array}\right]\\\\\left[\begin{array}{cc}-1&5\\2&0\end{array}\right]\left[\begin{array}{c}x_1\\x_2\end{array}\right]=\left[\begin{array}{c}2\\-4\end{array}\right][/tex]

[tex]\begin{cases}-1x_1+5x_2=2\\2x_1+0x_2=-4\end{cases}\\\begin{cases}-x_1+5x_2=2\\2x_1=-4\end{cases}\\\begin{cases}-x_1+5x_2=2\\x_1=-2\end{cases}\\\begin{cases}2+5x_2=2\\x_1=-2\end{cases}\\\begin{cases}5x_2=0\\x_1=-2\end{cases}\\\begin{cases}x_2=0\\x_1=-2\end{cases}[/tex]

[tex]\left[\begin{array}{cc}-1&5\\2&0\end{array}\right]\left[\begin{array}{c}-2\\0\end{array}\right]=\left[\begin{array}{c}2\\-4\end{array}\right]\\\\X=\left[\begin{array}{c}-2\\0\end{array}\right][/tex]