diff --git a/example/CMakeLists.txt b/example/CMakeLists.txt
index 3b54ae2..713d264 100644
--- a/example/CMakeLists.txt
+++ b/example/CMakeLists.txt
@@ -18,4 +18,5 @@ add_example(ex5 ON)
 add_example(ex6 ON)
 add_example(ex7 ON)
 add_example(ex8 ON)
-add_example(ex9 ON)
\ No newline at end of file
+add_example(ex9 ON)
+add_example(ex10 ON)
\ No newline at end of file
diff --git a/example/ex10.cpp b/example/ex10.cpp
new file mode 100644
index 0000000..f6dc1bf
--- /dev/null
+++ b/example/ex10.cpp
@@ -0,0 +1,64 @@
+/********************************************************
+ *  ██████╗  ██████╗████████╗██╗
+ * ██╔════╝ ██╔════╝╚══██╔══╝██║
+ * ██║  ███╗██║        ██║   ██║
+ * ██║   ██║██║        ██║   ██║
+ * ╚██████╔╝╚██████╗   ██║   ███████╗
+ *  ╚═════╝  ╚═════╝   ╚═╝   ╚══════╝
+ * Geophysical Computational Tools & Library (GCTL)
+ *
+ * Copyright (c) 2022  Yi Zhang (yizhang-geo@zju.edu.cn)
+ *
+ * GCTL is distributed under a dual licensing scheme. You can redistribute 
+ * it and/or modify it under the terms of the GNU Lesser General Public 
+ * License as published by the Free Software Foundation, either version 2 
+ * of the License, or (at your option) any later version. You should have 
+ * received a copy of the GNU Lesser General Public License along with this 
+ * program. If not, see <http://www.gnu.org/licenses/>.
+ * 
+ * If the terms and conditions of the LGPL v.2. would prevent you from using 
+ * the GCTL, please consider the option to obtain a commercial license for a 
+ * fee. These licenses are offered by the GCTL's original author. As a rule, 
+ * licenses are provided "as-is", unlimited in time for a one time fee. Please 
+ * send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget 
+ * to include some description of your company and the realm of its activities. 
+ * Also add information on how to contact you by electronic and paper mail.
+ ******************************************************/
+
+#include "gctl/core.h"
+#include "gctl/algorithm.h"
+#include "../lib/optimization.h"
+#include "iostream"
+#include "iomanip"
+
+using std::cout;
+using std::endl;
+using std::setw;
+
+int main(int argc, char const *argv[])
+{
+	gctl::matrix<double> A(4, 3);
+	for (int i = 0; i < A.row_size(); i++)
+	{
+		for (int j = 0; j < A.col_size(); j++)
+		{
+			A[i][j] = 3*(i+1) + j - 2;
+		}
+	}
+	A[3][1] = 1;
+
+    gctl::array<double> x(3), y(3), m(3);
+    x.random_float(-1.0, 1.0, gctl::RdUniform, 452);
+    gctl::matvec(y, A, x);
+
+	cout<<"A(" << A.row_size() << ", " << A.col_size() << ") = " <<endl;
+	A.show();
+
+	gctl::svd svdd;
+	svdd.decompose(A);
+    svdd.solve(y, m);
+
+    cout << "x = "; x.show();
+    cout << "m = "; m.show();
+	return 0;
+}
\ No newline at end of file
diff --git a/lib/optimization/svd.cpp b/lib/optimization/svd.cpp
index 85f125b..d863f9f 100644
--- a/lib/optimization/svd.cpp
+++ b/lib/optimization/svd.cpp
@@ -199,4 +199,27 @@ void gctl::svd::decompose(const matrix<double> &src_mat)
         else break;
     }
     return;
+}
+
+// solve for x in form Ax = b.  A is the original input matrix.
+// Note: b is modified in-place for row permutations
+void gctl::svd::solve(const array<double>& b, array<double> &x)
+{
+    if (b.empty())
+    {
+        throw domain_error("Invalid target vector. From gctl::svd::solve(...)");
+    }
+
+    x.resize(b.size());
+    array<double> t(K, 0.0);
+
+    matvec(t, U, b, NoTrans);
+
+    for (size_t i = 0; i < K; i++)
+    {
+        t[i] *= 1.0/S[i];
+    }
+
+    matvec(x, V, t, Trans);
+    return;
 }
\ No newline at end of file
diff --git a/lib/optimization/svd.h b/lib/optimization/svd.h
index 1e51ff5..d37b322 100644
--- a/lib/optimization/svd.h
+++ b/lib/optimization/svd.h
@@ -62,6 +62,14 @@ namespace gctl
 
         void decompose(const matrix<double> &src_mat);
 
+        /**
+         * @brief Solve for x in form Ax = b. A is the original input matrix.
+         * 
+         * @param b Right hang term of the linear system.
+         * @param x Return solution.
+         */
+        void solve(const array<double>& b, array<double> &x);
+
     protected:
         int maxi_iteration, K;
         double epsilon;