1. ## URGENT!

If A=
| |
| 5 e5 t sin(4 t) −5 e2 t cos(4 t)|
| |
| |
| −6 e5 t cos(4 t) −6 e2 t sin(4 t)|

then A^−1 is?

I need to find the inverse matrix of A, (A^-1) i've done it several times and have gotten the wrong answer (obviously, or i wouldn't be on here)
It's a homework quiz online that's due this evening, any help would be wonderful. thank you all

2. Originally Posted by williamb
If A=
| |
| 5 e5 t sin(4 t) −5 e2 t cos(4 t)|
| |
| |
| −6 e5 t cos(4 t) −6 e2 t sin(4 t)|

then A^−1 is?

I need to find the inverse matrix of A, (A^-1) i've done it several times and have gotten the wrong answer (obviously, or i wouldn't be on here)
It's a homework quiz online that's due this evening, any help would be wonderful. thank you all
do you mean $\displaystyle A = \left( \begin{array}{cc} 5e^{5t} \sin 4t & -5e^{2t} \cos 4t \\ & \\ -6e^{5t} \cos 4t & -6e^{2t} \sin 4t \end{array} \right)$ ?

obviously, since this is for a quiz we can't tell you the answer, but if the above is your matrix, note that following (which should be in your text):

if $\displaystyle M = \left( \begin{array}{cc} a & b \\ c & d \end{array} \right)$, then $\displaystyle M^{-1} = \frac 1{ad - bc} \left( \begin{array}{cc} d & -b \\ -c & a \end{array} \right) = \left( \begin{array}{cc} \frac d{ad - bc} & \frac {-b}{ad - bc} \\ & \\ \frac {-c}{ad - bc} & \frac a{ad - bc} \end{array} \right)$, provided $\displaystyle M$ is invertible, that is, its determinant $\displaystyle ad - bc$ is not zero