diff --git a/Lectures_my/NumMet/Lecture5/mchrzasz.log b/Lectures_my/NumMet/Lecture5/mchrzasz.log
index 22433e8..fa311e6 100644
--- a/Lectures_my/NumMet/Lecture5/mchrzasz.log
+++ b/Lectures_my/NumMet/Lecture5/mchrzasz.log
@@ -1,4 +1,4 @@
-This is XeTeX, Version 3.1415926-2.5-0.9999.3 (TeX Live 2013/Debian) (format=xelatex 2015.4.1)  18 SEP 2016 14:46
+This is XeTeX, Version 3.1415926-2.5-0.9999.3 (TeX Live 2013/Debian) (format=xelatex 2015.4.1)  1 OCT 2016 23:24
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diff --git a/Lectures_my/NumMet/Lecture5/mchrzasz.tex b/Lectures_my/NumMet/Lecture5/mchrzasz.tex
index ffb0471..dc897d4 100644
--- a/Lectures_my/NumMet/Lecture5/mchrzasz.tex
+++ b/Lectures_my/NumMet/Lecture5/mchrzasz.tex
@@ -273,7 +273,7 @@
 \end{align*}
 \ARROW Now there are many definitions of different norms... The most popular one (so-called ''column norm''):
 \begin{align*}
-\Vert A \vert_1 = \max_{1 \leq j \leq n} \sum_{i=1}^n \vert a_{i,j} \vert,
+\Vert A \Vert_1 = \max_{1 \leq j \leq n} \sum_{i=1}^n \vert a_{i,j} \vert,
 \end{align*}
 where $n$ -is the dimension of $A$, $i,j$ are columns and rows numbers.
 
@@ -290,7 +290,7 @@
 \Vert A \Vert_2 &= \sqrt{\rho(A^T A)}\\
 \rho(M) &= \max \lbrace \vert\lambda_i \vert: \det{M- \lambda I} =0,~i=1,...n \rbrace
 \end{align*}
-where $\rho(M)$ - spectral radios of $M$ matrix, $I$ unit matrix, $\lambda_i$ eigenvalues of $M$.\\
+where $\rho(M)$ - spectral radius  of $M$ matrix, $I$ unit matrix, $\lambda_i$ eigenvalues of $M$.\\
 
 \ARROW Row norm:
 \begin{align*}
@@ -343,7 +343,7 @@
 \end{align*}
 \ARROW So calculate the solutions one needs to calculate $n+1$ determinants. To calculate each determinate one needs $(n-1)n!$ multiplications. \\
 \ARROW Putting it all together one needs $(n+1)(n-1)n! = n^{n+2}$ \\
-\ARROW Brutal force but works ;)
+\ARROW Brute force but works ;)
 
 
 \end{small}