MHB 311.1.3.2 u+v and u-2v and tikx?

[karush]

$\tiny{311.1.3.2}$
Compute $u+v$ and $u-2v$
$u=\left[
\begin{array}{rr} 3\\2 \end{array}\right], v=\left[
\begin{array}{rr}2\\-1 \end{array}\right]
\quad u+v=\left[\begin{array}{rr}3+2\\2-1 \end{array}\right]=
\left[\begin{array}{rr}5\\4 \end{array}\right]
\quad u-2v=\left[\begin{array}{rr}3-2(2)\\2-2(-1) \end{array}\right]
=\left[\begin{array}{rr}1\\0 \end{array}\right]$

ok I think this is correct typos maybe, but the next question is

Display the vectors using arrows on an xy-graph
$u,v, -v, -2v, u+v, u-v, $ and $u-2v$

I was going to try this with tikx but was looking for an example to follow since we use arrows

also is these vectors $\mathbb{R}^2$

Mahalo

 

[skeeter]

$\tiny{311.1.3.2}$
Compute $u+v$ and $u-2v$
$u=\left[
\begin{array}{rr} 3\\2 \end{array}\right], v=\left[
\begin{array}{rr}2\\-1 \end{array}\right]
\quad u+v=\left[\begin{array}{rr}3+2\\2-1 \end{array}\right]=
\left[\begin{array}{rr}5\\4 \end{array}\right]
\quad u-2v=\left[\begin{array}{rr}3-2(2)\\2-2(-1) \end{array}\right]
=\left[\begin{array}{rr}1\\0 \end{array}\right]$

ok I think this is correct typos maybe, but the next question is

Display the vectors using arrows on an xy-graph
$u,v, -v, -2v, u+v, u-v, $ and $u-2v$

I was going to try this with tikx but was looking for an example to follow since we use arrows

also is these vectors $\mathbb{R}^2$

Mahalo

uhh ...

$u+v = \begin{bmatrix}
5\\ 1

\end{bmatrix}$

$u-2v = \begin{bmatrix}
-1\\ 4

\end{bmatrix}$

try again ...

 

[HOI]

I am hoping that you know, perfectly well, that 2- 1= 1, not 4, and, although it is slightly more complicated, that 2- 2(-1)= 4. not 0.

 

[karush]

$u=\left[
\begin{array}{rr} 3\\2 \end{array}\right], v=\left[
\begin{array}{rr}2\\-1 \end{array}\right]
\quad u+v=\left[\begin{array}{rr}3+2\\2-1 \end{array}\right]=
\left[\begin{array}{rr}5\\1 \end{array}\right]
\quad u-2v=\left[\begin{array}{rr}3-2(2)\\2-2(-1) \end{array}\right]
=\left[\begin{array}{rr}-1\\4 \end{array}\right]$

 

[skeeter]

$u=\left[
\begin{array}{rr} 3\\2 \end{array}\right], v=\left[
\begin{array}{rr}2\\-1 \end{array}\right]
\quad u+v=\left[\begin{array}{rr}3+2\\2-1 \end{array}\right]=
\left[\begin{array}{rr}5\\1 \end{array}\right]
\quad u-2v=\left[\begin{array}{rr}3-2(2)\\2-2(-1) \end{array}\right]
=\left[\begin{array}{rr}-1\\4 \end{array}\right]$

So ... what now?

 

[topsquark]

So ... what now?

Is there more to this problem?

-Dan

 

[karush]

how do you write a vector in tikz

 

[skeeter]

haven’t taken the time to learn tikz, but geogebra does a nice job and is user friendly ...

a = u+v
b = u-v
w = -v
d = -2v
c = u-2v

 

[I like Serena]

how do you write a vector in tikz

The following latex code does the job:

\begin{tikzpicture}
  \draw[->] (0,0) -- (3,2);
\end{tikzpicture}

\begin{tikzpicture}
\draw[->] (0,0) -- (3,2);
\end{tikzpicture}

A prettier version with some embellishments is:

\begin{tikzpicture}
  \coordinate[label=right:$\mathbf u$] (u) at (3,2);
  \draw[-latex, thick] (0,0) -- node[above left] {$\vec u$} (u);
\end{tikzpicture}

\begin{tikzpicture}
\coordinate[label=right:$\mathbf u$] (u) at (3,2);
\draw[-latex, thick] (0,0) -- node[above left] {$\vec u$} (u);
\end{tikzpicture}

 

[karush]

mahalo much
I'm trying to audit linear algrebra from UH west this spring but it will be via Google classroom so trying to get some early input

btw how do you get tikz to render on MHB

the reason I am using tikz is that will render in Overleaf which is commonly used here at UHW