sawdee said:I know how to solve systems, but the question asks to work backwards.
"Create a 4-d system that has a solution (-2,5,-6,1)."
How would i do this?
I like Serena said:Hi sawdee! Welcome to MHB! (Smile)
Without any other conditions, we can go for the simplest system that satisfies your requirement.
We can pick the system:
\begin{cases}
x_1=-2 \\
x_2 = 5 \\
x_3 = -6 \\
x_4 = 1
\end{cases}
No point in making it more complicated unless there are more restrictions.
We're talking about math - the simplest solution possible should be considered the best one.
sawdee said:Thank you! :) Happy to be here.
I picked that solution as well, but in terms of format I'm not sure how to set up the answer. Should I use a matrix with those 4 as my x values, and leave everything else as 0?
I think this is exactly what he wanted, thank you!I like Serena said:It depends a bit on what your teacher considers to be a "system".
If it's supposed to involve a matrix, we can pick the identity matrix with right hand values that correspond to the solution.
That is:
$$\begin{bmatrix}
1&0&0&0\\
0&1&0&0\\
0&0&1&0\\
0&0&0&1\\
\end{bmatrix}
\begin{bmatrix}
x_1\\
x_2\\
x_3 \\
x_4
\end{bmatrix} =
\begin{bmatrix}
-2 \\
5 \\
-6 \\
1
\end{bmatrix}$$
It's really just the same thing as the "system" I suggested though.
The only difference being what we pick as the notation.
A 4D system is a four-dimensional system that includes time as a fourth dimension in addition to the three spatial dimensions (length, width, and height). It is often used in scientific studies and simulations to better understand complex phenomena.
The process of coming up with a 4D system involves identifying the variables that affect the system and their relationships, determining the appropriate units for each dimension, and accounting for the element of time in the system. This can be achieved through mathematical modeling and simulation techniques.
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One of the main challenges in implementing a 4D system is collecting and analyzing data in four dimensions. This can be a complex and time-consuming process, requiring advanced technology and software. Another challenge is accurately representing and visualizing the data in a way that is understandable and meaningful.
A 4D system is often used in scientific research to study and analyze complex systems and phenomena. It allows scientists to simulate and predict the behavior of these systems over time, providing insights and advancements in various fields such as climate science, epidemiology, and astrophysics.