Keyword Analysis & Research: determine if columns are linearly independent


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Is column 1 linear or dependent?

In this matrix we know that column 1 is linear independent and columns 2 and 3 are dependent. I want something that always works, and I already have the SVD and QR decomposition implemented in Java and I hope one or both of them can help me solving this. Thanks in advance!

What does linear independent mean in a matrix?

When I say linear independent I mean not linearly dependent with any other column or any combination of other columns in the matrix. For example: In this matrix we know that column 1 is linear independent and columns 2 and 3 are dependent.

How to check if vectors are linearly independent?

Because we know that if det M ≠ 0, the given vectors are linearly independent. (However, this method applies only when the number of vectors is equal to the dimension of the Euclidean space.) det M = 12 ≠ 0 ⟹ linear independence of the columns. 206k 165 270 494 you can take the vectors to form a matrix and check its determinant.

Is column 2 a linear combination of columns 1 and 3?

Yes, column 2 is a linear combination of columns 1 and 3. Also, column 3 is a linear combination of columns 1 and 2. if you swap column 1 and 2 in my question matrix A, how do I then find which are linear dependant? Thanks for the help so far by the way!


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