linearly independent in a sentence

Examples

1. The dimension of a vector space is the maximum size of a linearly independent subset.
2. And with these two exponents, we get two different expansions that are linearly independent?
3. Such a system is always linearly independent.
4. This can be done if and only if " S " is linearly independent.
5. In contrast to the positive-definite case, these vectors need not be linearly independent.
6. And since T is linearly independent and S spans, we get n \ geq m.
7. Either those two vectors are linearly independent, or, err, they're not.
8. As a consequence, eigenvectors of " different " eigenvalues are always linearly independent.
9. The trivial case of the empty family must be regarded as linearly independent for theorems to apply.
10. is a solution of the same equation and is linearly independent from " y ".