Properties of Determinants

Posted In: Chemistry
  1. The value of determinant remains unchanged if rows are changed to columns and columns are changed to rows.
    $|\table a_1, a_2; b_1, b_2|=|\table a_1, b_1; a_1, b_2|$
  2. If two rows or two columns are interchanged, the sign of the determinant is changed.
    $|\table a_1, a_2; b_1, b_2|=-|\table b_1, b_2; a_1, a_2|$
  3. If two rows or two columns are identical, the value of teh determinant is zero.
    $|\table a_1, a_2; a_1, a_2|=0$
  4. if the elements of any row (or column) are multiplied by a common factor, the determinant is multiplied by that factor.
    $|\table ka_1, kb_1; a_2, b_2|=k|\table a_1, b_1; a_2, b_2|$
  5. If the elements of any row (or column) are increased (or decreased) by equal multiplies of the corresponding elements of any other row (or column), the value of the determinant is unchanged.
    $|\table a_1+kb_1, b_1; a_2+kb_2, b_2|=|\table a_1, b_1; a_2, b_2|$



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