document.write( "Question 343292: Show that in 3 x 3 determinant if one row is 0, the value of the determinant is 0 \n" ); document.write( "

Algebra.Com's Answer #245684 by Jk22(389) $\"\"$ $\"About$

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To compute the determinant, we can use, among other methods : \r
\n" ); document.write( "\n" ); document.write( "-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\r
\n" ); document.write( "\n" ); document.write( "-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. \n" ); document.write( "

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