1.5.41 Systems of Algebraic Equations

Condition: a system of linear equations \ (\ left \ {\ begin {array} {l} 2 x_ {1}+x_ {2} -x_ {3} = 1 \ \ x_ {1}+x_ {2}+x_2 x_ {4} = 2 \ \ 3 3 \ 2 \ 3 \ 3 \ 3 \ 3 \ 3 \ 3 \ 3 \ 3 \ 3 \ 3 \ 3 \ 3 \ 3 \ 3 \ 3 \ 3 \ 3 \ 3 x_ {1} +4 x_ {2} -2 x_ {4} = 3 \ end {array} \ right. b) find out whether the system is certain or uncertain; c) solve the system: write out a general solution, find a private solution and make a check for it.