Final answer:
If a matrix has more rows than columns, then the columns of the matrix are linearly independent.
Step-by-step explanation:
In linear algebra, if a matrix has more rows than columns, then the columns of the matrix are linearly independent.
To understand why this is true, let's consider a matrix A with m rows and n columns. Each column of A can be thought of as a linear combination of the n column vectors. If m > n, then there are more column vectors than the number of elements in each column vector. This means that there must be some redundancy or dependence among the column vectors, making them linearly dependent.
For example, if we have a matrix A with 4 rows and 3 columns, and the columns of A are linearly independent, it would mean that each column vector is unique and cannot be expressed as a linear combination of the other column vectors.