Question 343292: Show that in 3 x 3 determinant if one row is 0, the value of the determinant is 0
Answer by Jk22(389)   (Show Source):
You can put this solution on YOUR website! To compute the determinant, we can use, among other methods :
-the sum of the product of 1 elem. in every row/col. Hence every term in this sum contains a 0, since 1 elem has to be in the 0-row, and hence this sum is zero
-developing of the determinant with respect to this row: the sum of the product of the elements of this row times the sub-determinant remaining by deleting the element's row&col, times an alternating sign. Hence, this sum is a sum of zero times 2x2 determinants, hence zero.
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