addMult[A_,i_,c_,j_] := ( B = A; B[[i]] += c*B[[j]]; B);
addMultSlider[A_,i_,j_] := Manipulate[(
 B = addMult[A,i,t,j];
P = Parallelogram[{0,0},Transpose[B]] ;
GraphicsRow[
{MatrixForm[A],
MatrixForm[B],
 Graphics[{EdgeForm[Directive[Thick,Dashed,Blue]],Pink,P},
PlotRange->{{-5,5},{-5,5}}, Frame->True,PlotRangeClipping->True, ImageSize->300
]}]),
{{t,0,"Multiple added"},-5,5,0.1,Appearance->"Labeled"}
];

multRow[A_,i_,c_] := (B = A; B[[i]] *= c; B);
multRowSlider[A_,i_] := Manipulate[(
 B = multRow[A,i,t];
P = Parallelogram[{0,0},Transpose[B]] ;
GraphicsRow[
{MatrixForm[A],
MatrixForm[B],
 Graphics[{EdgeForm[Directive[Thick,Dashed,Blue]],Pink,P},
PlotRange->{{-5,5},{-5,5}}, Frame->True,PlotRangeClipping->True, ImageSize->300
]}]),
{{t,1,"Multiplier"},-5,5,0.1,Appearance->"Labeled"}
];

addMultSlider[{{2,-3},{1,2}},2,1]

addMultSlider[ {{2,-3},{1,2}},2,1]

addMultSlider[ {{2,-3},{0,3.5}},1,2]

multRowSlider[{{2,1},{0,1.5}},2]