Răspuns:
Explicație pas cu pas:
1. a) [tex]\left|\begin{array}{ccc}2&4\\-1&-2\end{array}\right | = 2*(-2) - 4*(-1) =-4+4=0[/tex]
b) M(x) = A+xB = [tex]\left[\begin{array}{ccc}2&4\\-1&-2\end{array}\right]+x\left[\begin{array}{ccc}-2&-6\\-1&3\end{array}\right] = \left[\begin{array}{ccc}2-2x&4-6x\\x-[tex]\left[\begin{array}{ccc}-6&-20\\3&10\end{array}\right]*\left[\begin{array}{ccc}-4&-14\\2&7\end{array}\right]*\left[\begin{array}{ccc}-2&-8\\1&4\end{array}\right] * \left[\begin{array}{ccc}0&-2\\0&1\end{array}\right] =[/tex]1&-2+3x\end{array}\right][/tex]
M(x) *M(1) = [tex]\left[\begin{array}{ccc}2-2x&4-6x\\-1+x&-2+3x\end{array}\right] *\left[\begin{array}{ccc}0&-2\\0&1\end{array}\right] = \left[\begin{array}{ccc}0&-2x\\0&x\end{array}\right]= x\left[\begin{array}{ccc}0&-2\\0&1\end{array}\right] =xM(1)[/tex]
c)M(4)M(3)M(2)M(1)= nM(1)
