Mat element wise multiplication 8UC1 x 8UC3

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both Mat's need the same number of channels for this, so you have to convert the 8UC1 one:

Mat uc1 = ...
Mat uc3;
cvtColor(uc1, uc3, COLOR_GRAY2BGR);

Mat res;
multiply(mat, uc3, res, CV_16UC3); // choose larger depth, to avoid saturation !