Răspuns:
Explicație pas cu pas:
1)
[tex]\Big A \cdot \Big B = \left(\begin{array}{cc}1&2\\2&3\end{array}\right) \cdot \left(\begin{array}{cc}a&b\\c&d\end{array}\right) =[/tex]
[tex]=\left(\begin{array}{cc}a+2c&b+2d\\2a+3c&2b+3d\end{array}\right) = \BIG I_2= \left(\begin{array}{cc}1&0\\0&1\end{array}\right)[/tex]
[tex]\left \{ {{\Big {a+2c = 1} \atop \Big {2a+3c = 0}} \right. \ \ \ \ \ \ \ \ \left \{{ \Big {b+2d = 0} \atop \Big {2b+3d = 1}} \right.[/tex]
[tex]2a = -3c\\a = \Big -\frac {3c}{2} \\-\frac {3c}{2}+ 2c = 1\\-3c + 4c = 2\\c = 2\\a = -\frac {3\cdot2}{2} = -3[/tex]
[tex]b+ 2d = 0\\b = -2d\\2\cdot(-2d) + 3d = 1\\-4d + 3d = 1\\-d = 1\\d = -1\\b= -2\cdot(-1)\\b = 2\\[/tex].
2)
[tex]\Big X_3 \cdot \Big X_7 = \left(\begin{array}{cc}1&0\\3&1\end{array}\right) \cdot \left(\begin{array}{cc}1&0\\7&1\end{array}\right) = \left(\begin{array}{cc}1+0&0+0\\3+7&0+1\end{array}\right) = \left(\begin{array}{cc}1&0\\10&1\end{array}\right) = \Big X_{10}[/tex]
