diff --git a/mlclass-ex1/gradientDescentMulti.m b/mlclass-ex1/gradientDescentMulti.m
index e5e1b7e..7fe7721 100644
--- a/mlclass-ex1/gradientDescentMulti.m
+++ b/mlclass-ex1/gradientDescentMulti.m
@@ -1,36 +1,35 @@
-function [theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters)
+function [theta, J_history] = gradientDescentMulti(X, y, theta, alpha, numberOfIterations)
 %GRADIENTDESCENTMULTI Performs gradient descent to learn theta
-%   theta = GRADIENTDESCENTMULTI(x, y, theta, alpha, num_iters) updates theta by
-%   taking num_iters gradient steps with learning rate alpha
+%   theta = GRADIENTDESCENTMULTI(x, y, theta, alpha, numberOfIterations) updates theta by
+%   taking numberOfIterations gradient steps with learning rate alpha
 
 % Initialize some useful values
 m = length(y); % number of training examples
-J_history = zeros(num_iters, 1);
+J_history = zeros(numberOfIterations, 1); 
 
-for iter = 1:num_iters
+for iteration = 1:numberOfIterations
+    % Perform a single gradient step on the parameter vector theta. 
 
-    % ====================== YOUR CODE HERE ======================
-    % Instructions: Perform a single gradient step on the parameter vector
-    %               theta. 
-    %
-    % Hint: While debugging, it can be useful to print out the values
-    %       of the cost function (computeCostMulti) and gradient here.
-    %
+    % we minimize the value of J(theta) by changing the values of the 
+    % vector theta NOT changing X or y
 
+    % alpha = learning rate as a single number
 
+    % hypothesis = mx1 column vector
+    % X = mxn matrix
+    % theta = nx1 column vector
+    hypothesis = X * theta;
 
+    % errors = mx1 column vector
+    % y = mx1 column vector
+    errors = hypothesis .- y;
 
-
-
-
-
-
-
-
-    % ============================================================
+    newDecrement = (alpha * (1/m) * errors' * X); 
+    
+    theta = theta - newDecrement';
 
     % Save the cost J in every iteration    
-    J_history(iter) = computeCostMulti(X, y, theta);
+    J_history(iteration) = computeCostMulti(X, y, theta);
 
 end