Question Number 88473 by M±th+et£s last updated on 10/Apr/20
Commented by kaivan.ahmadi last updated on 11/Apr/20
$${av}_{\mathrm{1}} +{b}\left({v}_{\mathrm{1}} +{v}_{\mathrm{2}} \right)+{c}\left({v}_{\mathrm{1}} +{v}_{\mathrm{2}} +{v}_{\mathrm{3}} \right)=\mathrm{0}\Rightarrow \\ $$$$\left({a}+{b}+{c}\right){v}_{\mathrm{1}} +\left({b}+{c}\right){v}_{\mathrm{2}} +{cv}_{\mathrm{3}} =\mathrm{0}\Rightarrow \\ $$$${c}=\mathrm{0} \\ $$$${b}+{c}=\mathrm{0}\Rightarrow{b}=\mathrm{0} \\ $$$${a}+{b}+{c}=\mathrm{0}\Rightarrow{a}=\mathrm{0} \\ $$$$\Rightarrow{these}\:{vectors}\:{are}\:{linearly}\:{indepwndent}. \\ $$
Commented by M±th+et£s last updated on 11/Apr/20
$${thank}\:{you}\:{sir} \\ $$