Problem $1.(50$ Points$)$

The mass and moment of inertia for the links of this slider$-$crank are given. A known force Facts on the slider block, and an unknown torque T acts on the crank. The angular velocity and acceleration of the crank are given as shown in polygons. Use matrix method to find the magnitude and the direction of the unknown torque. Based on the given angular velocity and acceleration of the crank, Consider the angular velocity and acceleration of all the links are known $($magnitudes and directions $-{}_2,{}_2$ and ${}_3$ are CCW$,$ and ${}_3$ is CW $).$