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And so we gots....

$Ba^(2+) + SO_4^(2-) rarr BaSO_4(s)darr$

...as the net ionic equation.

The magnesium and nitrate ions are along for the ride.....and stay in solution.

The complete metathesis reaction is....

$Ba(NO_3)_2(aq) + MgSO_4(aq) rarr BaSO_4(s)darr+Mg(NO_3)_2(aq)$

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