1.5.36 Systems of Algebraic Equations

Condition: given a homogeneous system of linear equations \ (\ left \ {\ begin {array} {c} x_ {1} +3 x_ {2}+x_} -4 x_ {4} = 0 \\ 2 x_ {1}+x_} +2 x_ {3} -3 -3 -3 -3 x_ {4} = 0 \\ 3 x_ {1} +4 x_ {2} +3 x_ {3} -7 x_ {4} = 0 \ end {array} \ right) find the rank of the system of the system; b) show that the system has a non -trivial solution; c) solve the system: write out a general solution, find a non -trivial private solution and make a check for it.