The value of `|[5^2 ,5^3, 5^4], [5^3, 5^4, 5^5], [5^4, 5^5, 5^6]|` is (a)`5^2` (b) 0 (c) `5^(13)` (d) `5^9`

Options

A. `5^(2)`
B. 0
C. `5^(13)`
D. `5^(9)`

Answer

B

Explanation

Let `Delta =|(5^(2),5^(3),5^(4)),(5^(3),5^(4),5^(5)),(5^(4),5^(5),5^(6))|`
`rArr Delta = 5^(2) xx5^(3) xx 5^(4) |(1,5,5^(2)),(1,5,5^(2)),(1,5,5^(2))| [("Taking"5^(2)"," 5^(3) and 5^(4)),("common from "R_(1).R_(2)),(and R_(3) " respectively")]`
`rArr Delta = 5^(9) xx 5 xx 5^(2) |(1,1,1),(1,1,1),(1,1,1)| [("Taing "5 and 5^(2) "common"),("from "C_(2) and C_(3) " respectively")]`
`rArr Delta = 5^(12) xx 0 = 0` [Using property 4]