Applied Linear Algebra |

Question

Question: Determine whether or not any column in the matrix is a linear combination of other columns. Provide a general method for answering the same question for any n x n matrix A.

My response:

Am I am in the right path or completely inaccurate?

Answer 1

This is good. When at least, one row or column is linear dependent, the matrix determinant is zero. In other words, when dimension is greater than the range of the matrix.

Answer 2

Almost correct. You say:

If $|A| = 0$, then each column is a linear combination of the other.

You should say:

If $|A| = 0$, then some column is a linear combination of some others.