Embibe Experts Solutions for Chapter: Matrices and Determinants, Exercise 1: AP EAPCET - 20 Aug 2021 Forenoon

$A=\left[\begin{array}{ccc}{a}^2& 15& 31\\ 12& b^2& 41\\ 35& 61& c^2\end{array}\right]$ and $B=\left[\begin{array}{ccc}2a& 3& 5\\ 2& 2b& 8\\ 1& 4& 2c-3\end{array}\right]$ are two matrices such that the sum of the principal diagonal elements of both $A$ and $B$ are equal, then the product of the principal diagonal elements of $B$ is

Let $Z_1,Z_2,Z_3$ be three non zero complex numbers such that $a=\left|Z_1\right|,b=\left|Z_2\right|,c=\left|Z_3\right|$. if the determinant $\left|\begin{array}{lll}a& b& c\\ b& c& a\\ c& a& b\end{array}\right|=0$, then

$\text{ The value of }\left|\begin{array}{ccc}b+c& a& a\\ b& c+a& b\\ c& c& a+b\end{array}\right|\text{ is }$

If $k\in R$ and $detA=\left|\begin{array}{lll}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|=K$ then $\det B=\left|\begin{array}{ccc}{a}_1& b_1& c_1\\ a_2+2a_1& b_2+2b_1& c_2+2c_1\\ a_3& b_3& c_3\end{array}\right|$ is equal to

If $\left|\begin{array}{lll}x& x^2& 1+x^3\\ y& y^2& 1+y^3\\ z& z^2& 1+z^3\end{array}\right|=0$ and $x, y, z$ are all distinct, then $xyz=$

Let $A,B,C,D$ be square real matrices such that $C^T=DAB, D^T=ABC, S=ABCD$, then $S^2$ is equal to

Let $A$ be a $n\times n$ matrix such that $A$ is upper-triangular. Then $adj\left(A\right)=$

If $A=\left[\begin{array}{cccc}\sqrt{2020}& \sqrt{2021}& \sqrt{2022}& \sqrt{2023}\\ \sqrt{4040}& \sqrt{4042}& \sqrt{4044}& \sqrt{4046}\\ \sqrt{6060}& \sqrt{6063}& \sqrt{6066}& \sqrt{6069}\\ \sqrt{8080}& \sqrt{8084}& \sqrt{8088}& \sqrt{8092}\end{array}\right]$ then the rank of $A$ is