1.5.38 Systems of Algebraic Equations

Condition: given a system of linear equations \ (\ left \ {\ begin {array} {l} 2 x_ {1}+x_ {2} -10 x_}+x_ {4} = 6 \ 3 x_ {1}+x_} -x_ {3}+x_ {4} = 3} = 3} = 3} = 3} = 3} = 3} = 3} = 3 \ 5 x_ {1} +2 x_ {2} -11 x_ {3} +2 x_ {4} = 9 \ end {array} \ right) to find the rank of an expanded matrix of the system and find out if the system is certain; b) solve the system: write out a general solution; c) Find a private solution of the system and do a check for it.