Matrices

A={{3,5,-1},{4,0,2},{-6,-3,2}}

MatrixForm[A]

B={{2,-2,3,1},{5,0,7,8},{9,-4,1,1}}

MatrixForm[B]

MatrixForm[A.B]

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

Note that {1,2,3} means a vector but {{1},{2},{3}} means a 3X1 matrix

MatrixForm[A]

B={{4,5,6}}

MatrixForm[B]

Dimensions[A]

Dimensions[B]

MatrixForm[A.B]

A={{3,0,7},{8,-1,5},{1,-9,4}}

MatrixForm[A]

MatrixForm[Transpose[A]]

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}}

MatrixForm[A]

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

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

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

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

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

A={{1,3,0},{2,6,4},{-1,0,2}}

MatrixForm[A]

Det[A]

B={{2,0,-4,6},{4,5,1,0},{0,2,6,-1},{-3,8,9,1}}

MatrixForm[B]

Det[B]

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

B=Inverse[A]

MatrixForm[A.B]