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

• MHB
• karush
In summary,The vectors $u+v$ and $u-2v$ are computed as $u=\left[\begin{array}{rr} 3\\2 \end{array}\right], v=\left[\begin{array}{rr}2\\-1 \end{array}\right]$.
karush
Gold Member
MHB
$\tiny{311.1.3.2}$
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

karush said:
$\tiny{311.1.3.2}$
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 ...

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.

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

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

So ... what now?

skeeter said:
So ... what now?
Is there more to this problem?

-Dan

how do you write a vector in tikz

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

karush said:
how do you write a vector in tikz

The following latex code does the job:
Code:
\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:
Code:
\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}

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

Last edited:

## 1. What do u+v and u-2v represent in 311.1.3.2?

u+v and u-2v represent mathematical operations in the context of 311.1.3.2. Specifically, u+v represents the sum of two numbers, u and v, while u-2v represents the difference between u and twice the value of v.

## 2. How do u+v and u-2v differ in their calculations?

The main difference between u+v and u-2v is the mathematical operation being performed. In u+v, we are adding two numbers together, while in u-2v, we are subtracting twice the value of v from u.

## 3. What is the purpose of using tikx in 311.1.3.2?

Tikx is a variable used in 311.1.3.2 to represent a third number in addition to u and v. It allows for a more general representation of mathematical operations and can be used in various calculations involving u and v.

## 4. Can u+v and u-2v be simplified further?

It depends on the values of u and v. In some cases, u+v and u-2v can be simplified by combining like terms or using other mathematical properties. However, in other cases, these expressions may not be able to be simplified any further.

## 5. How can understanding u+v and u-2v be applied in real-life situations?

The concepts of u+v and u-2v can be applied in various real-life situations, such as calculating distances, solving equations, and analyzing data. These operations are fundamental in mathematics and can be used in a wide range of fields, including science, engineering, and finance.

Replies
2
Views
2K
Replies
1
Views
955
Replies
1
Views
1K
Replies
14
Views
1K
Replies
5
Views
1K
Replies
3
Views
945
Replies
2
Views
812
Replies
1
Views
828
Replies
1
Views
993
Replies
3
Views
2K