One of the rules that won't change the value of a determinant of a matrix is: if we add to each element of one row, k times the corresponding element of another row, where k is ANY number (same statement applies to columns as well)(similar to row reduction, but applies to columns as well). I seem to be changng the value of the determinant by doing this... the first matrix i have(whose determinant is 0) is, 1st row: 0 -1 4, 2nd row: 1 0 -1, 3rd row: 4 1 0. I added -4 times the 2nd column to the first column(k= -4), and get, first row: 4 -1 4 , second row: 1 0 -1 , third row: 0 1 0. If u compute the determinant it is still zero! Now by using the above stated rule again, I add the 3rd column to the 1st column, (this theoretically should not change the value of the determinant, we take k=1), so the new matrix is, 1st row: 8 -1 4, 2nd row: 0 0 -1, 3rd row: 0 1 0. If we now solve for the determinant, we can see that it is 8. Why does this happen? It should still be zero!
2007-10-02
12:55:56
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1 answers
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asked by
John
6