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I am inclined to say it will not be invertible, since if one were to do singular value decomposition of a matrix, we would have a diagonal matrix as part of the decomposition, and this diagonal matrix would have 0 as an eigen value, and 1/0 is not allowed. Am I correct in my way of looking at it?

Also, does anyone know a good way to check if a given set of vectors (assume we just know we have a set, not their values) is linearly dependent or linearly independent without a calculator?

Thanks