Question Number 88552 by M±th+et£s last updated on 11/Apr/20
$${let}\:{W}_{\mathrm{1}} ,{W}_{\mathrm{2}} ,....,{W}_{{n}} \:{be}\:{subspaces}\:{of}\:{a}\:{vector} \\ $$$${space}\:{V}\:{over}\:{a}\:{field}\:\left({F},+,.\right) \\ $$$${prove}\:{that}: \\ $$$$\left(\mathrm{1}\right)\:{W}_{\mathrm{1}} \cap{W}_{\mathrm{2}} \cap....\cap{W}_{{n}} \:{a}\:{subspace} \\ $$$${of}\:{the}\:{vector}\:{space}\:{V}\:\:{over}\:\left({F},+,.\right). \\ $$$$\left(\mathrm{2}\right){W}_{\mathrm{1}} +{W}_{\mathrm{2}} +....+{W}_{{n}} \:{is}\:{subspace}\:{of}\:{the} \\ $$$${vector}\:{space}\:{V}\:{over}\:\left({F},+,.\right) \\ $$