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using cofactor method find the determinant

PostPosted: Thu 19 May, 2011 16:08
by barnamah
find the determinant of

Code: Select all
B =

     0     8     0     1
     0     7     3    -1
     3     0     0     2
     0    -5     0     6

how can should I proceed?

Solution:

choose a column with most zeros. I'll choose column 1 with the values:
Image
`[[0],[0],[3],[0]]`

from this column we can use only 3 because the other values are 0. 3 is located at row 3 column 1 `(-1)^(r+c)=(-1)^(1+3)=+1` so the sign for 3 is +.
Now using the first column with 3, we assume column 1 and row 3 (row 3 which has the 3 in it) does not exist and write our matrix:
Image
`| [8, 0, 1],[ 7, 3, -1],[ 0, 0, 2],[ -5, 0, 6]|`