Question

The square matrix

if and only if its column vectors are linearly independent.

Answer 1

Answer:

The answer is yes. Ax = b can be inconsistent in that situation. If the columns are independent, then either the matrix is square, or there are fewer columns than the number of rows. Where there are more columns than the number of rows, the columns cannot be linearly independent

Explanation:

Given a set of vectors, you can determine if they are linearly independent by writing the vectors as the columns of the matrix A, and solving Ax = 0. If there are any non-zero solutions, then the vectors are linearly dependent. If the only solution is x = 0, then they are linearly independent.