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diff --git a/191/CH4/EX4.13/Result4_13.txt b/191/CH4/EX4.13/Result4_13.txt
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+++ b/191/CH4/EX4.13/Result4_13.txt
@@ -0,0 +1,47 @@
+
+ A =
+
+ 1. 4. 2.
+ - 1. 2. 0.
+ 1. 3. - 1.
+
+ The X and A matrix :
+
+ 0.7071 0.7071 0.
+ - 0.7071 0.7071 0.
+ 0. 0. 1.
+
+ 1.4142 1.4142 1.4142
+ - 1.D-16 4.2426 1.4142
+ 1. 3. - 1.
+
+ The X and A matrix :
+
+ 0.8165 0. - 0.5774
+ 0. 1. 0.
+ 0.5774 0. 0.8165
+
+ 1.7321 2.8868 0.5774
+ - 1.D-16 4.2426 1.4142
+ 0. 1.633 - 1.633
+
+ The X and A matrix :
+
+ 1. 0. 0.
+ 0. 0.9333 - 0.3592
+ 0. 0.3592 0.9333
+
+ 1.7321 2.8868 0.5774
+ - 1.D-16 4.5461 0.7332
+ 4.D-17 0. - 2.032
+
+ Hence the original matrix can be decomposed as :
+
+ 0.5774 0.5133 - 0.635
+ - 0.5774 0.8066 0.127
+ 0.5774 0.2933 0.762
+
+ 1.7321 2.8868 0.5774
+ - 1.D-16 4.5461 0.7332
+ 4.D-17 0. - 2.032
+ \ No newline at end of file