--- a/docs/matrix.txt	Mon Sep 04 14:53:32 2017 -0700
+++ b/docs/matrix.txt	Mon Sep 04 15:06:38 2017 -0700
@@ -14,3 +14,21 @@
 
 `W1x1` gives some column vector, where `x1`
 is the first training example.
+
+Y = [ y1 y2 ... ym]
+
+For a two-layer network:
+
+dZ2 = A2 - Y
+
+dW = (1/m) dZ2 A1'
+
+db2 = (1./m)*np.sum(dZ2, axis=1, keepdims=True)
+
+dZ1 = W2' dZ2 * g1 ( Z1 )
+ : W2' dZ2 : an (n1, m) matrix
+ : * : element-wise product
+
+dW1 = (1/m) dZ1 X'
+
+db1 = (1/m) np.sum(dZ1, axis=1, keepdims=True)