Show that any three linear operators a, b, and ĉ satisfy the following (ja- cobi) identity (10 pt) [[a, b] ĉ] + [[b, c), a] + [[c, a, b) = 0

Three linear operators A,B, and C will satisfy the condition .

Explanation:

According to the question we have to prove.

Now taking Left hand side of the equation and solve.

Now use commutator property on it as,

Therefore, it is proved that .

freezing

deposition

condensation

explanation;

melting also called fusion is the process where solid becomes liquid, sublimation is the process where solid becomes gaseous without first changing to liquid, deposition involves change from gaseous to solid state, freezing involves change from liquid to solid, boiling or evaporation involves change of liquid to gaseous state, while condensation is the change from gaseous state to liquid state.

endothermic reactions involves absorption of heat from the surroundings or the environment while exothermic reactions involves loss of heat energy to the surroundings.

in this case, sublimation, evaporation and melting are endothermic reactions (gain energy from the environment) while, freezing, deposition and condensation are exothermic (loss of energy to the surroundings) reactions.