How do you solve this problem? Please show each step especially for to det and $10$ to the fifth.

$4\mathrm{.}15$: A slightly move sophistieated model of a vehiele suspension system is given in figure $P4\mathrm{.}15.$ Write the equations of motion in matrix form. Calculate the natural freqnencies for $k_1={10}^3\frac{N}{m},k_2={10}^4\frac{N}{m},m_2=50kg,$ and $m_1=2000kg.$

figwre $54\mathrm{.}17$