Finding Solution Set for Vectors

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In summary, a solution set for vectors is a set of all possible values for variables that satisfy a system of vector equations. To find the solution set, you can use elimination or substitution methods and plug in the values once the variables are solved for. There can be more than one solution set, which has applications in physics, computer graphics, and robotics. Finding the solution set is important in various fields as it allows for solving complex problems involving multiple variables and determining specific values that satisfy the equations.
  • #1
symsane
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How can I determine the solution set?

(1+2i)x1 + (1-i)x2 + x3 = 0,
ix1 + (1+i)x2 - ix3 = 0,
2ix1 + ix2 + (1+3i)x3 = 0.

Thanks..
 
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  • #2
Simply perform row-reduction to reduce the system to its row echelon form. The only difference with this and matrices containing only real numbers is that you can now multiply row by complex numbers as well.
 
  • #3
Or just solve the three equations the way you learned to solve linear equations way back. For example, subtracting 2 times the second equation from the third eliminates x1.
 

1. What is a solution set for vectors?

A solution set for vectors is a set of all possible values for the variables in a system of vector equations that satisfy the given equations.

2. How do you find the solution set for vectors?

To find the solution set for vectors, you can use elimination or substitution methods to solve the system of vector equations. Once you have solved for the variables, you can plug in the values to find the solution set.

3. Can there be more than one solution set for vectors?

Yes, there can be more than one solution set for vectors. This can occur if the system of equations has infinitely many solutions or no solutions at all.

4. What is the importance of finding the solution set for vectors?

Finding the solution set for vectors is important in many areas of science and engineering, such as physics, computer graphics, and robotics. It allows us to solve complex problems involving multiple variables and find the specific values that satisfy the given equations.

5. Are there any applications of finding the solution set for vectors?

Yes, there are many applications of finding the solution set for vectors. For example, it is used in determining the forces acting on an object in physics, creating 3D images in computer graphics, and calculating the motion of robots in engineering.

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