Let $a,b,c$ be such that $\left( {b + c} \right) \ne 0$ and $\left| {\begin{array}{*{20}{c}} a&{a + 1}&{a - 1}\\ { - b}&{b + 1}&{b - 1}\\ c&{c - 1}&{c + 1} \end{array}} \right|$ $ + {\left| {\begin{array}{*{20}{c}} {a + 1}&{b + 1}&{c - 1}\\ {a - 1}&{b - 1}&{c + 1}\\ {{{\left( { - 1} \right)}^{n + 2}}a}&{{{\left( { - 1} \right)}^{n + 1}}b}&{{{\left( { - 1} \right)}^n}c} \end{array}} \right|^1} = 0$ Then the value of $n$ is

JEE MATHEMATICS MCQ: MATRICES

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Let

a,b,c

be such that

\left( {b + c} \right) \ne 0

and

\left| {\begin{array}{cccccccccccccccccccc} a&{a + 1}&{a - 1}\\ { - b}&{b + 1}&{b - 1}\\ c&{c - 1}&{c + 1} \end{array}} \right|

+ {\left| {\begin{array}{cccccccccccccccccccc} {a + 1}&{b + 1}&{c - 1}\\ {a - 1}&{b - 1}&{c + 1}\\ {{{\left( { - 1} \right)}^{n + 2}}a}&{{{\left( { - 1} \right)}^{n + 1}}b}&{{{\left( { - 1} \right)}^n}c} \end{array}} \right|^1} = 0

Then the value of

n

View answer and explanation

Correct option: C

Any odd integer

The correct answer is C (Any odd integer). The given condition holds true only when n is an odd integer, making the second determinant the negative of the first.

JEE MATHEMATICS MCQ: MATRICES

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