MatrixForm[Inverse[(({{1, 0, 0}, {-1, 1, 0}, {-2, 0, 1}}))].Inverse[(({{1, 0, 0}, {0, 1, 0}, {0, 4.5, 1}}))]]

MatrixForm[(({{1, 0, 0}, {0, 1, 0}, {0, 4.5, 1}})).(({{1, 4, 1}, {0, 2, -2}, {0, -9, 0}}))]

L=(({{1.`, 0.`, 0.`}, {0.5`, 1.`, 0.`}, {0.5`, 0.69`, 1.`}}));
P={{0,0,1},{0,1,0},{1,0,0}};
y={y1,y2,y3};
b={7,13,5};
Solve[L.y==P.b,y]

{{y1->5.`,y2->10.5`,y3->-2.744999999999999`}}