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.
  • By solving the equations of transformation we obtain rE1 = a22x1 - a12x1, r = - a21x1 + allx2, aua12 where r = I = anon-anon; a21 a22 r is termed the determinant of substitution or modulus of transformation; we assure x 1, x 2 to be independents, so that r must differ from zero.
  • If the determinant is transformed so as to read by columns as it formerly did by rows its value is unchanged.