Initial value problem , system of equations involved , solve using Laplace transform

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Can anyone help me solve this problem, I could not find a similar solution on the web.

Solve the following problem : Initial value problem, System of equations involved , Using Laplace transform

$$ \vec{x}=\left[ \begin{array}{cc|c} 4&1\\ -4&6 \end{array} \right] $$

$$\vec{x}(0)= \left[ \begin{array}{cc|c} 1\\ -2 \end{array} \right] $$ Thanks in advance