1.5.52 Systems of Algebraic Equations
Condition: to explore the system of equations on components and certainty without solving it. Indicate the main (basic) and free variables. \ [\ left \ {\ begin {array} {c} x_ {1} +2 x_ {2} -3 x_ {3} -2 x_ {4} = 5 \\ -2 x_ {1}+x_ {3} +4 x_ {4} = 0 \\ -3 x_ {1} +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 x_ {2} +4 x_ {3} +3 x_ {4} =-11 \\ 13 x_ {1} -7 x_ {3} -9 x_ {4} = 35 \ end {Array} \ Right. \]
Solving Systems of Algebraic Equations by the Methods of Gauss, Jordan-Gauss, Cramer and Using the Inverse Matrix. Homogeneous and non-Homogeneous Systems of Equations.