Q : 5 Using the property of determinants and without expanding, prove that
Given determinant :
Splitting the third row; we get,
.
Then we have,
On Applying row transformation and then
;
we get,
Applying Rows exchange transformation and
, we have:
also
On applying rows transformation, and then
and then
Then applying rows exchange transformation;
and then
. we have then;
So, we now calculate the sum =
Hence proved.