Free thyroxine (free T4) tests are used to help evaluate thyroid function and diagnose thyroid diseases, including hyperthyroidism and hypothyroidism, usually after discovering that the thyroid stimulating hormone (TSH) level is abnormal. T4 and another hormone called triiodothyronine (T3) are produced by the thyroid gland.
[When the determinant of a matrix is nonzero, linear system it represents is linearly independent]. When the determinant of a matrix is zero, it rows are linearly dependent vectors, and its columns are linearly dependent vectors.
For homogeneous systems this happens precisely when the determinant is non-zero. We have now found a test for determining whether a given set of vectors is linearly independent: A set of n vectors of length n is linearly independent if the matrix with these vectors as columns has a non-zero determinant. The set is of course dependent if the determinant is zero.