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+function x = gauss (A, b)
+  issquare (A) || error ('Matrix A must be square');
+  Aug = [A b];
+  [m n] = size (Aug);
+  % forward elimination
+  for k = 1 : m - 1
+    for l = k + 1 : m
+      Aug(l, k:n) = Aug(l, k:n) - Aug(k, k:n)*Aug(l, k)/Aug(k, k);
+    end
+  end
+  x = ubst (Aug);
+end