From 971c8f80591621835e84e20f9d0e6b0f6941391a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andr=C3=A9=20Hensbergen?= <a.t.hensbergen@tudelft.nl>
Date: Mon, 12 Feb 2024 21:53:11 +0100
Subject: [PATCH] LastBitsBeforeEE1M2
---
Chapter5/DeterminantsViaRowReduction.md | 9 ++++++++-
Chapter7/LeastSquares.md | 5 ++---
2 files changed, 10 insertions(+), 4 deletions(-)
diff --git a/Chapter5/DeterminantsViaRowReduction.md b/Chapter5/DeterminantsViaRowReduction.md
index db3b26a..a6629ad 100644
--- a/Chapter5/DeterminantsViaRowReduction.md
+++ b/Chapter5/DeterminantsViaRowReduction.md
@@ -557,7 +557,14 @@ $$
\det{(A+B)} = \det{A}+\det{B}.
$$
-This statement is false. A trivial counterexample: $A = I$, $B = -I$.
+This statement is false. A trivial counterexample is given by $A = B = I_n$, for $n \geq 2$. Namely, for these matrices we see that
+
+<BR>
+
+$$
+ \det{A} + \det{B} = 1 + 1 = 2 \neq \det{(A+B)} = \det{(2I)} = 2^n.
+$$
+
</li>
<li>
diff --git a/Chapter7/LeastSquares.md b/Chapter7/LeastSquares.md
index 915c97a..d59d8d9 100644
--- a/Chapter7/LeastSquares.md
+++ b/Chapter7/LeastSquares.md
@@ -1117,10 +1117,9 @@ give a unique least squares solution, and it is $\hat{a} = 1.6$, $\hat{b} = 0.3
:::{figure} Images/Fig-LeastSquares-LSline.svg
:name: Fig:LeastSquares:LSline
-Least square line
-:::
-
+Least squares line
+:::
For the line $y = \hat{a} + \hat{b}x$ the sum of the squares of the residues becomes
--
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