Let $M=(a_{ij})_{3\times3}$, where $a_{ij}=\begin{cases}-1, & i=j\\ i^2-j^2, & i j\end{cases}$ $(i, j=1,2,3)$ If $X=\begin{bmatrix}1\\1\\1\end{bmatrix}$, then value of $-X^TMX$ is ________. (Here, $X^T$ denotes transpose of $X$).

JEE Main 2021 · MathsNumerical answerNumerical valueEasyCalculation

JEE Main 4 August 2021, Shift 1, Maths Q82

Question 82 of 90 in this shift, Maths question 22 of 30, Section B.

Let

M=(a_{ij})_{3\times3}

, where

a_{ij}=\begin{cases}-1, & i=j\\ i^2-j^2, & i<j\\ 2i-j, & i>j\end{cases}

(i, j=1,2,3)

X=\begin{bmatrix}1\\1\\1\end{bmatrix}

, then value of

-X^TMX

is ________. (Here,

X^T

denotes transpose of

X

Official answer

NTA final key.

Chapter: Matrices
Topic: Matrix Multiplication
Idea tested: Row-by-Column Multiplication

Same idea in other shifts

Asked 3× in all

26 Jul 2022, Shift 2 · Q3Let $A=\begin{bmatrix}1\\1\\1\end{bmatrix}$ and $B=\begin{bmatrix}9^2&-10^2&11^2\\12^2&13^2&-14^2\\-15^2&16^2&17^2\end{bmatrix}$ , then the…EasySingle correct
16 Mar 2021, Shift 2 · Q88Let $A=\begin{bmatrix}a_1\\a_2\end{bmatrix}$ and $B=\begin{bmatrix}b_1\\b_2\end{bmatrix}$ be two $2\times1$ matrices with real entries…MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.