Question

ex 1 a,b,c vă rog este foarte urgent dau 5 stele și ador pls ​

Answer 1

a) det a = (2 · 3) - (1 · 1) = 6 - 1 = 5

b)

$2\left[\begin{array}{ccc}2&1\\1&3\end{array}\right] - \left[\begin{array}{ccc}0&2\\2&2\end{array}\right] = \left[\begin{array}{ccc}4&2\\2&6\end{array}\right] - \left[\begin{array}{ccc}0&2\\2&2\end{array}\right] = \left[\begin{array}{ccc}4&0\\0&4\end{array}\right] = 2 \left[\begin{array}{ccc}2-0&0\\0&2\end{array}\right] \\= 2B(0)$

c)

$B(x)*B(1) - (x+1)A = \left[\begin{array}{ccc}2-x&x\\x&2\end{array}\right] * \left[\begin{array}{ccc}1&1\\1&2\end{array}\right] - (x+1) * \left[\begin{array}{ccc}2&1\\1&3\end{array}\right] = \left[\begin{array}{ccc}(2-x)*1+x*1&(2-x)*1+x*2\\x*1+2*1&x*1+2*2\end{array}\right] - \left[\begin{array}{ccc}2 (x+1)&x+1\\x+1&3(x+1)\end{array}\right] =$

$\left[\begin{array}{ccc}2&2+x\\x+2&x+4\end{array}\right] - \left[\begin{array}{ccc}2 (x+1)&x+1\\x+1&3(x+1)\end{array}\right] = \left[\begin{array}{ccc}-2x&1\\1&-2x+1\end{array}\right]$

det (B(x)*B(1) - (x+1)*A) = [-2x · (-2x+1) - 1] = 4x - 2x - 1 = 2x - 1

det (B(x)*B(1) - (x+1)*A) = 1 ⇒ 2x - 1 = 1 ⇒ 2x = 2 ⇒ x = 1