I was given a question, i am to use determinants to find out if the following 3 vectors are linearly independent. The following x's are columns but im not sure how to type out columns so they are posted as rows.
To use determinants you need a square matrix correct? and to do that i simply added a 4th column of 0,0,0,0. This would make the determinant 0 and mean the matrix is linearly independent? This seems way to easy, as if im overlooking something.
If the vectors are linearly dependent, then if you select any three columns, the rows of the resulting 3 x 3 matrix will still be dependent. So, to prove linear independence, it is sufficient to find three columns so that the determinant of the resulting matrix is nonzero.