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Mathematics · 2021

JEE Main · 4 August 2021, Shift 1 · Q82

Let M =(a_i j)_3 × 3, where a_i j= [-1, i=j, i^2-j^2, i<j, (i, j=1,2,3); 2 i-j, i>j. If X= [1; 1; 1], then value of -X^T M X is \ \ \ \. (Here, X^T…

Let $\displaystyle \mathrm{M}=\left(a_{i j}\right)_{3 \times 3}$, where $\displaystyle a_{i j}=\left[\begin{array}{ll}-1, & i=j, \\ i^2-j^2, & i<j, \quad(i, j=1,2,3) \\ 2 i-j, & i>j .\end{array}\right.$ If $\displaystyle X=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$, then value of $\displaystyle -X^T M X$ is \_\_\_\_. (Here, $\displaystyle \mathrm{X}^{\mathrm{T}}$ denotes transpose of X).
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.