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Determinante di $$$\left[\begin{array}{cc}e^{4 t} & e^{- \frac{7 t}{2}}\\4 e^{4 t} & - \frac{7 e^{- \frac{7 t}{2}}}{2}\end{array}\right]$$$
Calcolatore correlato: Calcolatore della matrice dei cofattori
Il tuo input
Calcola $$$\left|\begin{array}{cc}e^{4 t} & e^{- \frac{7 t}{2}}\\4 e^{4 t} & - \frac{7 e^{- \frac{7 t}{2}}}{2}\end{array}\right|$$$.
Soluzione
Il determinante di una matrice 2x2 è $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$.
$$$\left|\begin{array}{cc}e^{4 t} & e^{- \frac{7 t}{2}}\\4 e^{4 t} & - \frac{7 e^{- \frac{7 t}{2}}}{2}\end{array}\right| = \left(e^{4 t}\right)\cdot \left(- \frac{7 e^{- \frac{7 t}{2}}}{2}\right) - \left(e^{- \frac{7 t}{2}}\right)\cdot \left(4 e^{4 t}\right) = - \frac{15 e^{\frac{t}{2}}}{2}$$$
Risposta
$$$\left|\begin{array}{cc}e^{4 t} & e^{- \frac{7 t}{2}}\\4 e^{4 t} & - \frac{7 e^{- \frac{7 t}{2}}}{2}\end{array}\right| = - \frac{15 e^{\frac{t}{2}}}{2} = - 7.5 e^{\frac{t}{2}}$$$A