solve identity matrix

X = sym('X',[4,3]); % complex
[sizeX, sizeY]=size(X);
numZero = [1, 1, 2, 1];
if any(numZero == sizeY)
  error('no all zero row.')
end
zeroLoc = arrayfun(@(x) randsample(sizeY, x), numZero, 'uni', false);
count = histcounts(cat(1, zeroLoc{:}), 1:(sizeY+1));
if any(count == sizeX)
  error('no all zero col.')
end

zeroFunc = cell(sizeX, 1);
for i = 1:sizeX
  zeroFunc{i} = X(i, zeroLoc{i}) == 0;
end
zeroFunc = cat(2, zeroFunc{:});
idenMatFunc = X' * X == eye(sizeY);
Z = solve([idenMatFunc, zeroFunc], X);
% Z =
%
%     X1_1: [0x1 sym]
%     X2_1: [0x1 sym]
%     X3_1: [0x1 sym]
%     X4_1: [0x1 sym]
%     X1_2: [0x1 sym]
%     X2_2: [0x1 sym]
%     X3_2: [0x1 sym]
%     X4_2: [0x1 sym]
%     X1_3: [0x1 sym]
%     X2_3: [0x1 sym]
%     X3_3: [0x1 sym]
%     X4_3: [0x1 sym]