How much mechanical work is done in holding the brick 1m above the floor?

The mechanical work done in holding a brick 1 meter above the floor is zero, as work is defined as the force applied over a distance. While you exert an upward force equal to the weight of the brick to keep it suspended, there is no displacement in the direction of the force since you are not moving the brick. Thus, even though you are applying force, the lack of movement means no mechanical work is done.