Provide criticism for the following proof (it will appear on the comment box)

Let S = [v1,v2,...vn] be a set of n vectors in R^n(Rn). Let A be the matrix whose columns (rows) are the elements of S. Then S is linearly independent if and only if det(A) does NOT equal to zero.

Question

Provide criticism for the following proof (it will appear on the comment box)

Let S = [v1,v2,...vn] be a set of n vectors in R^n(Rn). Let A be the matrix whose columns (rows) are the elements of S. Then S is linearly independent if and only if det(A) does NOT equal to zero.

perl · Answer

is this in teh solution manual?

usukidoll · Answer

I'm typing it all down

usukidoll · Answer

it will come...

usukidoll · Answer

Suppose that S is linearly independent. Then it follows the reduced row form of A is In. Thus, A is row equivalent to In and hence det(A) doesn't equal to 0. Conversely, if det(A) doesn't equal to zero, then A is row equivalent to In. Now assume that the rows of A are linearly dependent. Then it follows that the reduced row echelon form of A has a zero row, which contradicts the earlier conclusion that A is row equivalent to In. Hence the rows of A are linearly independent.

usukidoll · Answer

This is the proof for columns only since the row version is too long or something. My professor hates this proof, so how do I give my criticism towards it besides the fact that in terms of English that this is a horrible written piece of garbage.

perl · Answer

S is a set of vectors? or a matrix

usukidoll · Answer

set of vectors

usukidoll · Answer

set of N vectors

perl · Answer

ok thanks
how did you find this solution manual

usukidoll · Answer

it's in my book. whatever I typed is already posted.

perl · Answer

can you find me solution manual for other books?

usukidoll · Answer

if you help me with this.

perl · Answer

In is the matrix |dw:1366613040566:dw|