How can solve system of equations by cramer's rule or LUDecomposition method in maple

Hi

How call each column of matrix by loop?

I am trying to plot f=[r^2 *cos(theta)+r*sin(theta)],as a DensityPlot[] in polar coordinates.

here r is a function of theta, r=r1(θ)..r2(θ) , for this reason, I have a problem to plot f in density plot

f=[r^2 *cos(theta)+r*sin(theta)];

r1(theta)= 0.3+0.1*cos(theta);
r2(theta)= 0.5+0.1*cos(theta);

display(changecoords(densityplot(f, r =r1(theta)..r2(theta), theta = 0 .. 2*Pi, style = patchnogrid, colorstyle = HUE), polar), axes = box, orientation = [270, 0], labels = [x, y, ``]);

(Error, (in plots/densityplot) bad range arguments r = .3+.1*cos(theta) .. .5+.1*cos(theta), theta = 0 .. 2*Pi )