Question

Se da matricea a(x)=(1+5x 10x/ -2x 1-4x)
REZOLVATI ECUATIA DET A(X)=1
CALCULAȚI A(1) SI A(1) LA puterea a 2a

Answer 1

Răspuns:

Explicație pas cu pas:

det(A)=(1+5x)·(1-4x)-(-2x)·10x=1-4x+5x-20x²+20x²=1+x, deci 1+x=1, deci x=0

$A(1)=\left[\begin{array}{ccc}1+5*1&10*1\\-2*1&1-4*1\\\end{array}\right] =\left[\begin{array}{ccc}6&10\\-2&-3\\\end{array}\right] \\(A(1))^{2}=\left[\begin{array}{ccc}6&10\\-2&-3\\\end{array}\right] *\left[\begin{array}{ccc}6&10\\-2&-3\\\end{array}\right] =\left[\begin{array}{ccc}6*6+10*(-2)&6*10+10*(-3)\\-2*6+(-3)*(-2)&-2*10+(-3)*(-3)\\\end{array}\right] =\left[\begin{array}{ccc}16&30\\-6&-11\\\end{array}\right]$