Invertability as a substitute for looking for linear independence

ichigo444
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Can i use the invertability of a matrix as an alternative way of determining the linear independence of a set? Thank you.
 
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Yes. If the columns of the matrix are considered to be vectors, these vectors are linearly independent iff the matrix is invertible.
 
If you suppose the set creates a matrix A, then you can say the set is linearly independent if Ax = 0 has only the trivial solution. If A is invertible then x = A-1 0 = 0 is the only solution and the set is linearly independent.
 
Mark44 said:
Yes. If the columns of the matrix are considered to be vectors, these vectors are linearly independent iff the matrix is invertible.

This is true for a square matrix. A non-square matrix is obviously not invertible but can be made of linearly independent vectors.
 

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