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Question
If A = `[(1,2,3),(2,"a",2),(5,7,3)]` is a singular matrix , find the value of 'a'.
Solution
∵ A is a singular matrix.
|A| = 0
`|(1,2,3),(2,"a",2),(5,7,3)|`
`= 1 xx |("a",2),(7,3)| - 2 |(2,2),(5,3)| + 3 |(2,"a"),(5,7)|`
= (3a - 14) - 2 (-4) + 3 (14 - 5a)
= 36 - 12a
∴ 36 - 12a = 0
⇒ a = 3
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