The value of |(2 y(1)z(1),y(1) z(2) + y(...

The value of `|(2 y_(1)z_(1),y_(1) z_(2) + y_(2) z_(1),y_(1) z_(3) + y_(3) z_(1)),(y_(1) z_(2) y_(2) z_(1),2y_(2) z_(2),y_(2) z_(3) + y_(3) z_(2)),(y_(1) z_(3) + y_(3) z_(1),y_(2) z_(3) + y_(3) z_(2),2y_(3) z_(3))|`, is

`y_(1) y_(2) y_(3) z_(1) z_(2) z_(3)`

`y_(1) + y_(2) + y_(3)`

`z_(1) + z_(2) + z_(3)`

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The correct Answer is:

We have,
`|(2 y_(1) z_(1),y_(1) z_(2) + y_(2) z_(1),y_(1) z_(3) + y_(3) z_(1)),(y_(1) z_(2) + y_(2) z_(1),2y_(2) z_(2),y_(2) z_(3) + y_(3) z_(2)),(y_(1) z_(3) + y_(3) z_(1),y_(2) z_(3) + y_(3) z_(2),2y_(3) z_(3))|`
`= |(y_(1) z_(1) + y_(1) z_(1),y_(1) z_(2) + y_(2) z_(1),y_(1) z_(3) + y_(3) z_(1)),(y_(1) z_(2) + y_(2) z_(1),y_(2) z_(2) + y_(2) z_(2),y_(2) z_(3) + y_(3) z_(2)),(y_(1) z_(3) + y_(3) z_(1),y_(2) z_(3) + y_(3) z_(2),y_(3) z_(3) + y_(3) z_(3))|`
`= |(y_(1),z_(1),0),(y_(2),z_(2),0),(y_(3),z_(3),0)||(z_(1),y_(1),0),(z_(2),y_(2),0),(z_(3),y_(3),0)| = 0 xx 0 = 0`

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