v1 = {-8, 7, 6, 5, -7};

    
v2 = {8, -7, -9, -5, 7};

    
v3 = {-8, 7, 4, 5, -7};

    
v4 = {1, 4, 9, 6, -7};

    
v5 = {-9, 3, -4, -1, 0}

MatrixForm[{v1, v2, v3, v4, v5}]

MatrixForm[Transpose[{v1, v2, v3, v4, v5}]]

MatrixForm[RowReduce[Transpose[{v1, v2, v3, v4, v5}]]]

v3 - (5/3) v1 - (2/3) v2

v5 - (4/3) v1 - (1/3) v2 + v4

MatrixForm[RowReduce[Transpose[{v1, v2, v4}]]]

MatrixForm[Transpose[{v5, v4, v3, v2, v1}]]

MatrixForm[RowReduce[Transpose[{v5, v4, v3, v2, v1}]]]

Transpose[{{2, 2, -1}, {-5, -5, 4}, {0, 1, 0}}]

Transpose[{{4/3, 1/3, -1}, {0, 0, 1}, {5/3, 2/3, 0}}]

Transpose[{{2, 2, -1}, {-5, -5, 4}, {0, 1, 0}}] . 
      Transpose[{{4/3, 1/3, -1}, {0, 0, 1}, {5/3, 2/3, 0}}]