The Molecular Equation is as follow,
Ba(NO₃)₂ ₍aq₎ + MgSO₄ ₍aq₎ → BaSO₄ ₍s₎ + Mg(NO₃)₂ ₍aq₎
The Total Ionic Equation is as follow,
Ba²⁺₍aq₎ + 2NO₃⁻ ₍aq₎ +Mg²⁺ ₍aq₎ + SO₄²⁻ ₍aq₎ → Mg²⁺ ₍aq₎ + 2NO₃⁻ ₍aq₎ + BaSO₄ ₍aq₎
Here, Mg²⁺ and NO₃⁻ are spectator Ions,
So,
The Net Ionic Equation is as follow,
Ba²⁺ ₍aq₎ + SO₄²⁻ ₍aq₎ → BaSO₄ ₍aq₎