 Theorem 4. If all the elements of a row (or column) are multiplied by the same number, as k, the determinant is multiplied by k. For...  A College Algebra - Page 493by Henry Burchard Fine - 1904 - 595 pagesFull view - About this book
 | Henry Burchard Fine - Algebra - 1904 - 616 pages
...Therefore D=- D, that is, 2 D = 0, or D = 0. Thus, aad bbe с с / = abf + aec + dbc — aec — abf — dbc = 0. Theorem 4». If all the elements of a, row...be simplified by applying this theorem. Thus, - 6 8 2 -341 -11 15-20 6=2-5- 3-4 1=2-6. 3-4- 1-1 1 =480. 3 4-1 4-1 1 -1 903 904 905 906 907 Corollary.... | |
 | Ernest Julius Wilczynski - Algebra - 1916 - 542 pages
...228.) Similarly for interchange of two columns according to the final theorem of Art. 229. 4. If all of the elements of a row {or column) are multiplied by the same factor m, the determinant is multiplied by m. PROOF. Of the elements which are multiplied by m, one... | |
 | Ernest Brown Skinner - Algebra - 1917 - 288 pages
...determinant is equal to zero. For every term of the expansion contains a factor from the row of zeros. THEOREM 4. If all the elements of a row (or column) are multiplied by a constant k, '' \ determinant is multiplied by k. For every term of the exp. -1 sion is multiplied... | |
 | William Fogg Osgood, William Caspar Graustein - Geometry, Analytic - 1921 - 650 pages
...transformation and evaluation of determinants. They lead up to a simple proof of Theorem 2. THEOREM 3. If all the elements of a row (or column) are multiplied by the same quantity, the value of the determinant is multiplied by this quantity. For, each term of a determinant... | |
 | 1926 - 912 pages
...interchange rows and columns. The sign of D is changed if two contiguous rows or columns are interchanged. If all the elements of a row or column are multiplied by a constant K, the new determinant obtained has the value KD. The infinite determinant 0 1 1 ± 1 0... | |
 | Lloyd Leroy Smail - Processes, Infinite - 1925 - 192 pages
...interchange rows and columns. The sign of D is changed if two contiguous rows or columns are interchanged. If all the elements of a row or column are multiplied by a constant K, the new determinant obtained has the value KD. The infinite determinant 0 1 1 ± 1 0... | |
 | Karl John Holzinger - Education - 1928 - 396 pages
...of lower order. Multiplying each row by the reciprocals of the items in the first columns, we have (If all the elements of a row (or column) are multiplied by the same number n, the determinant is multiplied by n.) RECIPROCAL OP COLUMN 1 COLUMN 1 1 1 0.54 0.49 0.41 X 1.000... | |
 | Henry Burchard Fine - Mathematics - 18?? - 648 pages
...Therefore D = — D, that is, 2 D = 0, or D = 0. aad Thus, bbe ce/ = abf + aec + dhc — aec — abf — dbc = 0. Theorem 4. If all the elements of a row (or...often be simplified by applying this theorem. Thus, -682 _34i -11 15-20 6 3 4-1 = 2-6 3-4 4 -1 = 2.6.3.4 1-1 = 480. 903 904 A COLLEGE ALGEBRA 905 906 907... | |
 | D. P. Acharjya - Computer science - 2007 - 314 pages
...on evaluating D, using first column elements we get D,= flil fl.,, «; 31 fl12 a22 a32 Property 2. If all the elements of a row (or column) are multiplied by a constant k, then the determinant so obtained is k times of the original determinant. ie, '11 "12... | |
 | 308 pages
...same manner it can be proved that if two rows or columns are identical or proportional, .4=0; that if all the elements of a row or column are multiplied by k, the value of the new determinant is kA ; that columns and rows may be interchanged, keeping the... | |
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