Question

Se considera matricele A(2 1)
6 3. Și X(a) = I2+aA ,unde a este un număr real.
a) arătați că A^2=5A
b) calculați det (X(a)).

Answer 1

[tex] 5 * \left[\begin{array}{cc}2&1\\6&3\end{array}\right] = \left[\begin{array}{cc}10&5\\30&15\end{array}\right] A^{2} = \left[\begin{array}{cc}2&1\\6&3\end{array}\right] * \left[\begin{array}{cc}2&1\\6&3\end{array}\right] = \left[\begin{array}{cc}4+6&2+3\\12+18&6+9\end{array}\right] = \left[\begin{array}{cc}10&5\\30&15\end{array}\right] [/tex]

Prin Urmare A^2 = 5 * A

[tex] \left[\begin{array} {cc}1&0\\0&1\end{array}\right] + \left[\begin{array}{cc}2a&a\\6a&a\end{array}\right] = \left[\begin{array}{cc}2a+1&a\\6a&a+1\end{array}\right] det(x) = 2a^2 + 2a + a + 1 - 6a^2 = -4a^2 + 3a + 1 [/tex]

Posibil am gresit la det am facut in cap calculele, de acolo ai o ecuatie de grad 2