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Question
If f(x) = `|(0, x - "a", x - "b"),(x + "b", 0, x - "c"),(x + "b", x + "c", 0)|`, then ______.
Options
f(a) = 0
f(b) = 0
f(0) = 0
f(1) = 0
Solution
If f(x) = `|(0, x - "a", x - "b"),(x + "b", 0, x - "c"),(x + "b", x + "c", 0)|`, then f(0) = 0.
Explanation:
f(x) = `|(0, x - "a", x - "b"),(x + "b", 0, x - "c"),(x + "b", x + "c", 0)|`
⇒ f(0) =`|(0, -"a", -"b"),("a", 0, -"c"),("b", "c", 0)|`
Which is skew-symmetric determinant of order 3
Hence f(0) = 0.
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