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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 - Mathematics

Sum

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`

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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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