Why i'm getting different results from RGB to XYZ color conversion?

Hello,

I'm performing a color conversion from RGB to XYZ using 3 methods. The first one is the MATLAB suggested function

IM_XYZ = rgb2xyz(IM_ORIG);

The second one is another bult in matlab function

cform = makecform('srgb2xyz');
IM_XYZ2 = applycform(IM_ORIG,cform);

The third one I did it myself using the the matrix used in Lindbloom website (inside one of the functions that the rgb2xyz() function calls i could find the same matrix and even the Lindbloom website reference).

The problem is that i'm getting different results from the 3 ways.

Can someone help me?

Thanks

All my code:

clc;
clear;
close all

%%Generate test image

R = [255 0 0; 255 0 85; 22 34 115];
G = [0 255 0; 255 0 85; 82 12 85];
B = [0 0 255; 255 0 85; 101 66 22];

IM_ORIG(:,:,1) = R;
IM_ORIG(:,:,2) = G;
IM_ORIG(:,:,3) = B;

IM_ORIG = (IM_ORIG)./255;

%%Converte imagem RGB para XYZ

IM_XYZ = rgb2xyz(IM_ORIG); % first method

cform = makecform('srgb2xyz');
IM_XYZ2 = applycform(IM_ORIG,cform);  % second method

% conversion matrix (http://www.brucelindbloom.com/index.html?Eqn_RGB_XYZ_Matrix.html)
M_conv = [0.4124564  0.3575761  0.1804375; ... 
          0.2126729  0.7151522  0.0721750; ... 
          0.0193339  0.1191920  0.9503041];

RGB(:) = IM_ORIG(1,1,:);

aa = M_conv*(RGB');

for i = 1:size(IM_ORIG,1)
    for j = 1:size(IM_ORIG,2)
        RGB(:) = IM_ORIG(i,j,:);
        IM_XYZ3(i,j,:) = (M_conv*(RGB'))'; 
    end
end

[KARSH THARYANI]

Are you sure that the input to both the functions is absolute, in the sense that the RGB spectrum format for an image is relative(sRGB is different from RGB). Hence, if one function assumes input as RGB and the other as sRGB, is it not possible that their conversion outputs might be different?

Also, in your method 3 it seems that you are not making R_srgb to R_linear, as stated in the Wikipedia article here