Sentence Examples

  • Consideration of the definition of the determinant shows that the value is unaltered when the suffixes in each element are transposed.
  • If any two rows or any two columns of a determinant be identical the value of the determinant is zero.
  • Resultant Expressible as a Determinant.-From the theory of linear equations it can be gathered that the condition that p linear equations in p variables (homogeneous and independent) may be simultaneously satisfied is expressible as a determinant, viz.
  • If the determinant is transformed so as to read by columns as it formerly did by rows its value is unchanged.
  • X n / I l yl, y2,���yn Theorem.-If the functions y 1, y2,��� y n be not independent of one another the functional determinant vanishes, and conversely if the determinant vanishes, yl, Y2, ...y.