diff --git a/.gitignore b/.gitignore
index e5ea43dda1308f2817d718324ba06721d7d8d511..f492b0da4fa3769f638349a6e6b1222f87ac374a 100644
--- a/.gitignore
+++ b/.gitignore
@@ -135,4 +135,4 @@ $RECYCLE.BIN/
 .DS_Store?
 ._*
 .Spotlight-V100
-.Trashes
\ No newline at end of file
+.Trashes._logger_
diff --git a/hello-world/checkpoint_epoch0.pth b/hello-world/checkpoint_epoch0.pth
index deb132b204f2d7670ec67cfb741f3f27fa8ee2bc..a6ac4c80d00e448a1aaeb87c044f01b6c0202869 100644
Binary files a/hello-world/checkpoint_epoch0.pth and b/hello-world/checkpoint_epoch0.pth differ
diff --git a/hello-world/checkpoint_epoch4.pth b/hello-world/checkpoint_epoch4.pth
index 50f30235e748e9c6a599e339bfa77281c31a4268..0575140bca3533bda2c500f2d6ea75d96b2f1934 100644
Binary files a/hello-world/checkpoint_epoch4.pth and b/hello-world/checkpoint_epoch4.pth differ
diff --git a/hello-world/main.py b/hello-world/main.py
index 1e366010f1d0c99174d816da2b93de373c4f3aca..4c7c6e56a217643a7afe33ad8f9ed0cbd5da53f5 100644
--- a/hello-world/main.py
+++ b/hello-world/main.py
@@ -1,6 +1,11 @@
-import torch
 import numpy as np
 
-np_array = np.array([1, 2, 3])
-tensor = torch.from_numpy(np_array)
-print(tensor)
\ No newline at end of file
+# 定义矩阵 A 和向量 b
+A = np.array([[1, 1], [1, 2], [1, 3]])  # 设计矩阵（3x2）
+b = np.array([1, 2, 2])                # 观测值（3x1）
+
+# 求解最小二乘问题
+x, residuals, rank, singular_values = np.linalg.lstsq(A, b, rcond=None)
+
+print("最优解 x:", x)
+print("残差平方和:", residuals)
\ No newline at end of file