If (A= [ array lll 2 & 0 & 0 2 & 2 & 0 2 & 2 & 2 array ]), then (adj(adj A)) is equal to -

Correct answer: B. (16 [ array lll 1 & 0 & 0 1 & 1 & 0 1 & 1 & 1 array ]) (|A|= [ array lll 2 & 0 & 0 2 & 2 & 0 2 & 2 & 2 array ]=(2)(2)(2)=8) Now adj ((adj A)=| A|^ 3-2 ~A (=8 [ array lll 2 & 0 & 0 2 & 2 & 0 2 & 2 & 2 array ]=16 [ array ccc 1 & 0 & 0 1 & 1 & 0 1 & 1 & 1 array ])

BITSAT 2011

Exam: BITSAT
Year: 2011
Subject: Mathematics
Chapter: Matrices

BITSAT 2011 · Mathematics · Matrices

If (A= [ array lll 2 & 0 & 0 2 & 2 & 0 2 & 2 & 2 array ]), then...

If (A=

\left[

\begin{array}{lll}2 & 0 & 0 \\ 2 & 2 & 0 \\ 2 & 2 & 2\end{array}

\right]), then (\operatorname{adj}(\operatorname{adj} A)) is equal

to -

Options

A(8 $\left[$ $\begin{array}{lll}1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1\end{array}$ $\right])
B(16 $\left[$ $\begin{array}{lll}1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1\end{array}$ $\right])
C(64 $\left[$ $\begin{array}{lll}1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1\end{array}$ $\right])
DNone of these

Correct answer

B. (16 $\left[$ $\begin{array}{lll}1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1\end{array}$ $\right])

Step-by-step solution

(|A|=

\left[

\begin{array}{lll}2 & 0 & 0 \\ 2 & 2 & 0 \\ 2 & 2 & 2 \end{array}

\right]=(2)(2)(2)=8) Now adj ((\operatorname{adj} A)=|

\mathrm{A}|^{3-2}

\mathrm{~A}

(=8

\left[

\begin{array}{lll}2 & 0 & 0 \\ 2 & 2 & 0 \\ 2 & 2 & 2 \end{array}

\right]=16 \left[

\begin{array}{ccc}1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{array}

$\right])

Practice Matrices on Quantrex Academy →

More from Matrices

If A=(1)/(3)[ array ccc 1 & 2 & 2 2 & 1 & -2 a & 2 & b array ] is an orthogonal matrix… BITSAT 2024 If matrix A=[ array ccc 3 & -2 & 4 1 & 2 & -1 0 & 1 & 1 array ] and A^ -1 =(1)/(k) adj(A)… BITSAT 2024 If A and B are symmetric matrices of same order such that A B+B A=X and A B-B A=Y , then… BITSAT 2024 If A=[ array cc 1 & 0 0 & -1 array ], P=[ array ll 1 & 1 0 & 1 array ] and X=A P A^T… BITSAT 2024 If A is a square matrix of order 3 , then Adj(Adj.A^2) = BITSAT 2024 If A= [ array ccc 0 & c & -b -c & 0 & a b & -a & 0 array ] and B= [ array ccc a² & a b &… BITSAT 2023 If A=[ array cc 0 & 2 3 & -4 array ] and k A=[ array cc 0 & 3 a 2 b & 24 array ] , then… BITSAT 2023 Let A=[ array ccc 1 & -1 & 1 2 & 1 & -3 1 & 1 & 1 array ] and 10 B=[ array ccc 4 & 2 & 2… BITSAT 2022 If [ array cc 1 & - θ θ & 1 array ][ array cc 1 & θ - θ & 1 array ]^ -1 =[ array cc a &… BITSAT 2022 If A is an 3 × 3 non- singular matrix, such that AA^ ' = A^ ' A and B = A^ - 1 A^ '… BITSAT 2019 If P = [ cases a & b & c b & c & a c & a & b cases ] , abc = 1 , P^ T P = I then the… BITSAT 2018 Let M bea 3 × 3 n × n -singular matrix with det(M)=α . If [M^ -1 . adj ( adj ( M )]= KI… BITSAT 2015 If [ array cc α & β γ & -α array ] is square root of identity matrix of order 2 then - BITSAT 2014 If A=[ array ll 1 & 1 1 & 1 array ] then ^ 100 : BITSAT 2014 Let A=[ array ll 0 & α 0 & 0 array ] and (A+I)^ 50 -50 A=[ array ll a & b c & d array ]… BITSAT 2012 The matrix A²+4 A-5 I , where I is identity matrix and A= [ array cc 1 & 2 4 & -3 array ]… BITSAT 2011 Full Matrices list Matrices JEE Maths PYQs JEE Mathematics PYQs All BITSAT PYQs