If $A$ is a singular matrix then $ADJ A$ is

Important Questions on Matrices and Determinants

EASY

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 17 - Matrices and Determinants>Exercise 1>Q 138

If $a+b+c=0$, one root of $\left|\begin{array}{ccc}a-x& c& b\\ c& b-x& a\\ b& a& c-x\end{array}\right|=0$ is

MEDIUM

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 17 - Matrices and Determinants>Exercise 1>Q 139

Suppose $D=\left|\begin{array}{lll}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|$ and $D^{\text{'}}=\left|\begin{array}{lll}{a}_1+p{b}_1& b_1+q{c}_1& c_1+r{a}_1\\ a_2+p{b}_2& b_2+q{c}_2& c_2+r{a}_2\\ a_3+p{b}_3& b_3+q{c}_3& c_3+r{a}_3\end{array}\right|$, then

EASY

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 17 - Matrices and Determinants>Exercise 1>Q 140

If $A$ and $B$ are two non-zero square matrices such that $AB=0$, then

MEDIUM

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 17 - Matrices and Determinants>Exercise 1>Q 141

The method of solving square systems of linear equations using determinants is due to

MEDIUM

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 17 - Matrices and Determinants>Exercise 1>Q 142

If $A=\left[\begin{array}{cc}3& 1\\ -1& 2\end{array}\right]$ then $A^2=$

MEDIUM

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 17 - Matrices and Determinants>Exercise 1>Q 143

If $A=\left[\begin{array}{cc}4& x+2\\ 2x-3& x+1\end{array}\right]$ is symmetric then $X=$

EASY

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 17 - Matrices and Determinants>Exercise 1>Q 144

If $\left|\begin{array}{lll}1& 2& 3\\ 2& x& 3\\ 3& 4& 5\end{array}\right|=0$ then $x=$

MEDIUM

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 17 - Matrices and Determinants>Exercise 1>Q 145

$\left|\begin{array}{lll}x& 1& y+z\\ y& 1& z+x\\ z& 1& x+y\end{array}\right|=$