Let A = [ array ll 1 1 1 array ] and B = [ cases 9 ^ 2 & - 10 ^ 2 & 11 ^ 2 12 ^ 2 & 13 ^ 2 & - 14 ^ 2 - 15 ^ 2 & 16 ^ 2 & 17 ^ 2 cases ] , then the value of A ^ ' BA is;

Correct answer: D. 539 Given A = [ array ll 1 1 1 array ] and B = [ cases 9 ^ 2 & - 10 ^ 2 & 11 ^ 2 12 ^ 2 & 13 ^ 2 & - 14 ^ 2 - 15 ^ 2 & 16 ^ 2 & 17 ^ 2 cases ] then A ^ ' = [ cases 1 & 1 & 1 cases ] So A ^ ' B = [ cases 1 & 1 & 1 cases ][ cases 9 ^ 2 & - 10 ^ 2 & 11 ^ 2 12 ^ 2 & 13 ^ 2 & - 14 ^ 2 - 15 ^ 2 & 16 ^ 2 & 17 ^ 2 cases ] = [ cases 9 ^ 2 + 12 ^ 2 - 15 ^ 2 & - 10 ^ 2 + 13 ^ 2 + 16 ^ 2 & 11 ^ 2 - 14 ^ 2 + 17 ^ 2 cases ] = [ cases 0 & 325 & 214 cases ] Now A ^ ' BA = [ cases 0 & 325 & 214 cases ][ array ll 1 1 1 array ] = [325 + 214] = [539]

JEE Main 202226 JulyEvening Shift

Exam: JEE Main
Year: 2022
Date: 26 July
Shift: Evening Shift
Subject: Mathematics
Chapter: Matrices

JEE Main 2022 · 26 July · Evening Shift · Mathematics · Matrices

Let A = [ array ll 1 1 1 array ] and B = [ cases 9 ^ 2 & - 10 ^ 2 &...

Let

A = \left[

\begin{array}{ll}1 \\ 1 \\ 1\end{array}

\right] and

B = \left[

\begin{cases}{9}^{2} & - {10}^{2} & {11}^{2} \\ {12}^{2} & {13}^{2} & - {14}^{2} \\ - {15}^{2} & {16}^{2} & {17}^{2}\end{cases}

\right]

, then the value of

{A}^{'}BA$ is;

Options

A $1224$
B $1042$
C $540$
D $539$

Correct answer

D. $539$

Step-by-step solution

Given $A = \left[$ $\begin{array}{ll}1 \\ 1 \\ 1\end{array}$ $\right]$ and $B = \left[$ \begin{cases}{9}^{2} & - {10}^{2} & {11}^{2} \\ {12}^{2} & {13}^{2} & - {14}^{2} \\ - {15}^{2} & {16}^{2} & {17}^{2}\end{cases} $\right]$
then ${A}^{'} = \left[$ \begin{cases}1 & 1 & 1\end{cases} $\right]$
So ${A}^{'}B = \left[$ \begin{cases}1 & 1 & 1\end{cases} $\right]\left[$ \begin{cases}{9}^{2} & - {10}^{2} & {11}^{2} \\ {12}^{2} & {13}^{2} & - {14}^{2} \\ - {15}^{2} & {16}^{2} & {17}^{2}\end{cases} $\right]$
$= \left[$ \begin{cases}{9}^{2} + {12}^{2} - {15}^{2} & - {10}^{2} + {13}^{2} + {16}^{2} & {11}^{2} - {14}^{2} + {17}^{2}\end{cases} $\right]$
$= \left[$ \begin{cases}0 & 325 & 214\end{cases} $\right]$
Now ${A}^{'}BA = \left[$ \begin{cases}0 & 325 & 214\end{cases} $\right]\left[$ $\begin{array}{ll}1 \\ 1 \\ 1\end{array}$ $\right]$
$= \left[325 + 214\right]$
$= \left[539\right]$

Practice Matrices on Quantrex Academy →

More from Matrices