MATLAB help finding a set of linearly independent vectors

In summary, to determine if a set of vectors is linearly independent, one can set up the equations c1*v1 + c2*v2 + c3*v3 = 0 and solve for c1, c2, and c3 using a matrix and the variable k. This can be done by expanding all three equations and using symbolic solving.
  • #1
gibxam
12
0
If I'm given a set of vectors
{-4; 3; -10} = v1
{2; -2; -3+k} = v2
{2; -6; 14} = v3
I want to find that they are linearly independent if and only if k != something

to solve this is simple but a huge tedious pain (although not nearly as tedious as trying to find a solution to this question)

I just solve:

c1*v1 + c2*v2 + c3*v3 = 0
or
Ax = 0 where a is matrix above

I'm desperately trying to convince MATLAB that k is a variable but can't do it. I've tried making it symbolic with syms but it doesn't work. Please help me. Thank you
 
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  • #2
You should try expanding all three equations and having symbolic solve them simultaneously rather than using the cell format you have above.
 

1. What is the purpose of finding a set of linearly independent vectors in MATLAB?

Finding a set of linearly independent vectors in MATLAB is important for many applications in science and engineering. It allows us to represent complex systems or data in a simpler and more efficient way, making it easier to analyze and manipulate. Additionally, linearly independent vectors are necessary for solving systems of equations and performing other mathematical operations in MATLAB.

2. How do I determine if a set of vectors is linearly independent in MATLAB?

To determine if a set of vectors is linearly independent in MATLAB, we can use the rref function. This function reduces a matrix to its reduced row echelon form and checks for any rows with all zeros. If there are no rows with all zeros, then the vectors are linearly independent. Another method is to check if the determinant of the matrix formed by the vectors is non-zero. If the determinant is non-zero, then the vectors are linearly independent.

3. Can I find a set of linearly independent vectors for any matrix in MATLAB?

Yes, it is possible to find a set of linearly independent vectors for any matrix in MATLAB. However, the process may be more complex for matrices with a high number of dimensions or for matrices that are not square. It is important to carefully consider the properties of the matrix and the desired outcome before attempting to find a set of linearly independent vectors.

4. Are there any built-in functions in MATLAB for finding a set of linearly independent vectors?

Yes, there are several built-in functions in MATLAB that can help with finding a set of linearly independent vectors. These include the rref function, which we can use to determine if a set of vectors is linearly independent, and the rank function, which returns the rank of a matrix and can be used to determine the minimum number of linearly independent vectors needed to span the same space as the matrix.

5. Can I use MATLAB to find a set of linearly independent vectors for data analysis?

Yes, MATLAB can be used for data analysis and can help find a set of linearly independent vectors for a given dataset. This can be particularly useful for dimensionality reduction, where we want to represent data in a lower-dimensional space while retaining as much information as possible. By finding a set of linearly independent vectors, we can reduce the dimensionality of our data without losing important information.

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