# [SOLVED]311.1.3.2 u+v and u-2v and tikx?

#### karush

##### Well-known member
$\tiny{311.1.3.2}$
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

##### Well-known member
MHB Math Helper
$\tiny{311.1.3.2}$
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 ...

#### Country Boy

##### Well-known member
MHB Math Helper
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

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

#### skeeter

##### Well-known member
MHB Math Helper
$u=\left[ \begin{array}{rr} 3\\2 \end{array}\right], v=\left[ \begin{array}{rr}2\\-1 \end{array}\right] \quad u+v=\left[\begin{array}{rr}3+2\\2-1 \end{array}\right]= \left[\begin{array}{rr}5\\1 \end{array}\right] \quad u-2v=\left[\begin{array}{rr}3-2(2)\\2-2(-1) \end{array}\right] =\left[\begin{array}{rr}-1\\4 \end{array}\right]$
So ... what now?

MHB Math Helper

#### karush

##### Well-known member
how do you write a vector in tikz

#### skeeter

##### Well-known member
MHB Math Helper
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

#### Klaas van Aarsen

##### MHB Seeker
Staff member
how do you write a vector in tikz
The following latex code does the job:
LaTeX:
\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:
LaTeX:
\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

##### Well-known member
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

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