Factoring Imaginary Numbers in a 2x1 Matrix: Solving the Physics Problem

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SUMMARY

The discussion centers on the challenge of factoring a 2x1 matrix containing imaginary numbers, specifically the matrix represented as \left(\begin{array}{cc}1+\sqrt{3}\\1-\sqrt{3}\end{array}\right). Participants emphasize that the resulting matrix should only contain 0's, 1's, or imaginary units (i), which can be negative. The conversation explores whether subtracting the rows could simplify the matrix, but consensus indicates that the solution may not exist in the desired form, suggesting the possibility of a spurious solution.

PREREQUISITES
  • Understanding of complex numbers and imaginary units
  • Familiarity with matrix operations, specifically 2x1 matrices
  • Basic knowledge of linear algebra concepts
  • Proficiency in LaTeX for mathematical representation
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  • Research methods for simplifying matrices with complex numbers
  • Study the properties of imaginary numbers in linear algebra
  • Explore techniques for identifying spurious solutions in mathematical problems
  • Learn about matrix row operations and their implications
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Students and professionals in physics, mathematics, and engineering who are dealing with complex matrices and seeking to understand the implications of imaginary numbers in matrix operations.

NutriGrainKiller
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This is a physics problem but I am having trouble factoring this matrix. Basically, there shouldn't be anything left inside the matrix except 0's, 1's, or i's (any of which can be negative). This seems like such an easy problem but I cannot find something that works.

Any ideas?

<br /> <br /> \frac {1} {2\sqrt{2}}<br /> <br /> \left(\begin{array}{cc}1+\sqrt{3}\\1-\sqrt{3}\end{array}\right)<br /> <br />

in case anyone finds this confusing this is a 2 row 1 column matrix.
 
Last edited:
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bumping because i just now got the latex to display properly
 
couldnt you simply subract the rows from each other??
 
Basically, there shouldn't be anything left inside the matrix except 0's, 1's, or i's (any of which can be negative).
Why do you think it can be put into that form?
 
stunner5000pt said:
couldnt you simply subract the rows from each other??

No I don't think so

Hurkyl said:
Why do you think it can be put into that form?

because the inside can only result in one of several cases, all of which contain only 0's, 1's, or imaginary numbers. anything else wouldn't make sense
 
because the inside can only result in one of several cases, all of which contain only 0's, 1's, or imaginary numbers. anything else wouldn't make sense
Then maybe this is a spurious solution. What were you actually solving?
 
Last edited:

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