Assertion: determinant's row | /r/HasProperty | column
Facets:
Source sentences:
text: A determinant does not change if the elements of one row (column) are multiplied by an arbitrary constant and added to the elements of another row (column); thus, for example,
text: Designating any element of the matrix by the symbol a r c (the subscript r identifies the row and c the column), the determinant is evaluated by finding the sum of n!
text: It is also possible to consider matrices with infinitely many rows and/or columns even if, being infinite objects, one cannot write down such matrices explicitly.
text: A determinant does not change if the elements of one row (column) are multiplied by an arbitrary constant and added to the elements of another row (column); thus, for example,
text: A determinant does not change if the elements of one row (column) are multiplied by an arbitrary constant and added to the elements of another row (column); thus, for example,
text: A determinant does not change if the elements of one row (column) are multiplied by an arbitrary constant and added to the elements of another row (column); thus, for example,
text: A determinant does not change if the elements of one row (column) are multiplied by an arbitrary constant and added to the elements of another row (column); thus, for example,
text: A determinant does not change if the elements of one row (column) are multiplied by an arbitrary constant and added to the elements of another row (column); thus, for example,
text: This property can be proved by using the definition of determinant For every permutation , we have that because the product contains one entry from each row (column), but one of the rows (columns) contains only zeros.
text: multiply a row (column) by a non-zero constant;
text: add a multiple of a row (column) to another row (column);
text: add a multiple of a row (column) to another row (column);
text: The first element (row 1, column 1) is always a +
text: Also remember that there are three elementary row (column) operations:
text: This property can be proved by using the definition of determinant For every permutation , we have that because the product contains one entry from each row (column), but one of the rows (columns) contains only zeros.
text: interchange two rows (columns).