Question

With the numbers 2, 4, 6, 8, all the
possible determinants with these four
different elements are constructed.
What is the sum of the values of all
such determinants?​

Answer 1

Given :  numbers 2, 4, 6, 8

To Find :   all the possible determinants with these four different elements are constructed.

sum of the values of all such determinants

Solution:

4 elements can be arranged in 4 !  ways = 24  way

2 * 4  -  6 * 8  =     - 40   ( 4 times )  as these can be  

( 4 * 2 - 6 * 8  or  2 *  4 - 8 * 6  =  4 * 2 -  8 * 6 )

Similarly

2 * 6  -   4 * 8  =   - 20    ( 4 times )

2 * 8  - 4 * 6  =   - 8    ( 4 times)

4 * 6   -  2 * 8   =  8   ( 4 times)

4 * 8  - 2 * 6   =   20    ( 4 times)

6 * 8  -  2 * 4  = 40   ( 4 times)

Sum of values of all such determinants = 0  

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