Hi, while trying to visually find if a 3x3 matrix is linearly dependent or independent, in one of the examples I assumed correct that the matrix is singular cuz column 1 and column 2 are the same, instead of finding the relation between the rows, so can someone confirm whether this was just a coincidence or are we supposed to look for dependency between both rows and columns?
Even after thinking for a while I think my way of comparing columns to determine singularity or non-singularity was correct cuz i think if in a 3x3 matrix if any two rows are the same then depending on the 3rd column and constant we would either have redundancy or contradiction and never completeness, which i think is absolutely correct.
can somebody confirm?
If the determinant of a matrix is 0, then it is singular.
For a square matrix a non trivial relation among columns imply non trivial relations among rows. In fact, the dimension of the space spanned by columns and rows are the same (true even for non square matrices). In your example if you subtract the second row from the first, you get the third row.
Simply put, for a square matrix checking relations among columns is the equivalent to checking relations among rows.
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