Math & Data Science Q&A - Get answers from our AI that are verified by human experts
First time here? Checkout the FAQs!
x

*Math Image Search only works best with zoomed in and well cropped math screenshots. Check DEMO

MathsGee Android Q&A


0 like 0 dislike
227 views
Give a real life and practical application of linear combinations of vectors
in Mathematics by Platinum (164,290 points) | 227 views

1 Answer

0 like 0 dislike
Best answer

Colors on computer monitors are commonly based on what is called the RGB color model. Colors in this system are created by adding together percentages of the primary colors red $(\mathrm{R})$, green $(\mathrm{G})$, and blue (B). One way to do this is to identify the primary colors with the vectors
$$
\begin{array}{ll}
\mathbf{r}=(1,0,0) & \text { (pure red) } \\
\mathbf{g}=(0,1,0) & \text { (pure green) } \\
\mathbf{b}=(0,0,1) & \text { (pure blue) }
\end{array}
$$
in $R^{3}$ and to create all other colors by forming linear combinations of $\mathbf{r}, \mathbf{g}$, and $\mathbf{b}$ using coefficients between 0 and 1 , inclusive; these coefficients represent the percentage of each pure color in the mix.

The set of all such color vectors is called RGB space or the RGB color cube (Figure 3.1.14). Thus, each color vector c in this cube is expressible as a linear combination of the form
$$
\begin{aligned}
\mathbf{c} &=k_{1} \mathbf{r}+k_{2} \mathbf{g}+k_{3} \mathbf{b} \\
&=k_{1}(1,0,0)+k_{2}(0,1,0)+k_{3}(0,0,1) \\
&=\left(k_{1}, k_{2}, k_{3}\right)
\end{aligned}
$$
where $0 \leq k_{i} \leq 1 .$ As indicated in the figure, the corners of the cube represent the pure primary colors together with the colors black, white, magenta, cyan, and yellow. The vectors along the diagonal running from black to white correspond to shades of gray.

cube

by Platinum (164,290 points)

Related questions

0 like 0 dislike
1 answer
0 like 0 dislike
1 answer
0 like 0 dislike
0 answers
1 like 0 dislike
1 answer
asked Jul 28, 2022 in Mathematics by MathsGee Platinum (164,290 points) | 88 views
0 like 0 dislike
0 answers
asked Jun 3, 2019 in Mathematics by MathsGee Platinum (164,290 points) | 232 views
1 like 0 dislike
1 answer
asked Dec 29, 2022 in Mathematics by Edzai Zvobwo SIlver Status (11,090 points) | 16 views
0 like 0 dislike
1 answer
asked Jan 26, 2022 in Mathematics by MathsGee Platinum (164,290 points) | 207 views
0 like 0 dislike
1 answer
0 like 0 dislike
1 answer
asked Jan 28, 2022 in Mathematics by MathsGee Platinum (164,290 points) | 319 views
1 like 0 dislike
1 answer
0 like 0 dislike
0 answers
1 like 0 dislike
1 answer

Join MathsGee and get expert-verified answers to your maths and data science questions fast. We use a combination of generative AI and human experts to provide you the best answers to your questions. Ask a question now!


On the MathsGee, you can:


1. Ask and answer questions


2. Get expert-verified answers


3. Vote on questions and answers


4. Tip your favorite community members


5. Join expert live video sessions (Paid/Free)


6. Earn points by participating


7. Start a Fundraiser



Posting on MathsGee


1. Remember the human


2. Act like you would in real life


3. Find original source of content


4. Check for duplicates before publishing


5. Read the community guidelines




MathsGee Rules


1. Answers to questions will be posted immediately after moderation


2. Questions will be queued for posting immediately after moderation


3. Depending on the number of messages we receive, you could wait up to 24 hours for your message to appear. But be patient as posts will appear after passing our moderation.




MathsGee Android Q&A

MathsGee Android Q&A