A point in the robot gripper frame$$ P $[4,4,4]$ is subjected to following transformation. Find the coordinates of the new point$$ P$*$ relative to the reference frame at the conclusion of$$ transformation.

Step $1.$ Translation of$5$ units along z axis followed by translation of $4$ units along X$-$axis.

Step $2.$ Rotation of $30$ degrees around X$-$axis

Step $3.$ Followed by translation of $7$ units along X axis.

Find the transformation matrix for the concatenated transformation and co$-$ordinates of the final position of the point?