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Question
Using properties of determinants, find the value of x for which
`|(4-"x",4+"x",4+"x"),(4+"x",4-"x",4+"x"),(4+"x",4+"x",4-"x")|= 0`
Solution
Given:
`|(4-"x",4+"x",4+"x"),(4+"x",4-"x",4+"x"),(4+"x",4+"x",4-"x")|= 0`
R1 → R1 + R2 +R3
`|(12+"x",12+"x",12+"x"),(4+"x",4-"x",4+"x"),(4+"x",4+"x",4-"x")|= 0`
Take (12 +x) common
`(12+"x")|(1,1,1),(4+"x",4-"x",4+"x"),(4+"x",4+"x",4-"x")|= 0`
C2 → C2 - C1, C3 → C3 - C1
`(12+"x")|(1,0,0),(4+"x",-2"x",0),(4+"x",0,-2"x")|= 0`
(12 + x) (-2x) (-2x) = 0
⇒ x = 0, -12
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