Manipulate[
A={{2, 0, 0},{0, 1, 0}, {0, 0,1}};
c = Transpose[{{i,2, 1}}];
x=A.c;
{MatrixForm[x], " = ", MatrixForm[A] , MatrixForm[c] },
{i,0,10, 1}]

Manipulate[
{
A={{Cos[0.1], -Sin[0.1], 0},{Sin[0.1], Cos[0.1], 0}, {0, 0,1}};
c = Transpose[{{i,2, 1}}];
x=A.c;
MatrixForm[x], " = ", MatrixForm[A] , MatrixForm[c] },
{i, 0, 10, 1}
]