7.3 Linear Systems of Equations

A={{-3,8},{8,-12}}

A.{x,y}=={5,-11}

Solve[%,{x,y}]

A={{1,-1,1},{-1,1,-1},{0,10,25},{20,10,0}}

A.{x1,x2,x3}=={0,0,90,80}

Solve[%,{x1,x2,x3}]

LinearSolve[A,{0,0,90,80}]

RowReduce[{{1,-1,1,0},{-1,1,-1,0},{0,10,25,90},{20,10,0,80}}]

MatrixForm[%]

A={{3,2,2,-5,8},{0.6,1.5,1.5,-5.4,2.7},{1.2,-0.3,-0.3,2.4,2.1}}

RowReduce[A]

MatrixForm[%]

A={{3,2,1},{2,1,1},{6,2,4}}

LinearSolve[A,{3,0,6}]

B={{3,2,1,3},{2,1,1,0},{6,2,4,6}}

RowReduce[B]

A={{-2,-17,4,3},{7,0,3,-2},{0,2,8,-6},{5,-13,-1,5}}

MatrixForm[A]

LinearSolve[A,{0,0,-20,16}]

A.{w,x,y,z}=={0,0,-20,16}

Solve[%,{w,x,y,z}]

A={{0,4,-2},{6,-2,1},{4,8,-4}}

LinearSolve[A,{2,29,24}]

A.{x,y,z}=={2,29,24}

Solve[%,{x,y,z}]

A={{2,1,-3},{5,0,2},{8,-1,7}}

A.{x,y,z}=={8,3,0}

Solve[%,{x,y,z}]

LinearSolve[A,{8,3,0}]

A={{5,-2},{-1,4}}

A.{x,y}=={20.9,-19.3}

Solve[%,{x,y}]