2.78 Given a set of linear equations automatically generate the matrix A and vector b and solve \(A x=b\)

Problem: Given

\[{\begin {array} [c]{ccc}4x+4y+2z & = & 12\\ 5x+6y+3z & = & 7\\ 9x+7y+10z & = & 9 \end {array}} \]

Automatically convert it to the form \(Ax=b\) and solve

Mathematica Remove["Global`*"] eqs = {4x+3y+2z==12, 5x+6y+3z ==7, 9x+7y+10z ==9}; {b,a} = CoefficientArrays[eqs,{x,y,z}]; Normal[a]//MatrixForm	\[ \left ( {\begin {array}{ccc} 4 & 3 & 2 \\ 5 & 6 & 3 \\ 9 & 7 & 10 \\ \end {array}} \right ) \]
Normal[b]//MatrixForm	\[ \{-12,-7,-9\} \]
LinearSolve[a,-b]//N	{6.71429,-2.85714,-3.14286}

 

Maple restart; eqs:=[4*x+3*y+2*z=12,5*x+6*y+3*z=7,9*x+7*y+10*z=9]; A,b := LinearAlgebra:-GenerateMatrix(eqs,[x,y,z]); LinearAlgebra:-LinearSolve(A,b)

\[ \left [\begin {array}{c} \frac {47}{7} \\ -\frac {20}{7} \\ -\frac {22}{7} \end {array}\right ] \]