Matrices And Determinants Ques 42
Consider the set $A$ of all determinants of order $3$ with entries $0$ or $1$ only. Let $B$ be the subset of $A$ consisting of all determinants with value $1$ . Let $C$ be the subset of $A$ consisting of all determinants with value $-1$ . Then,
(a) $C$ is empty
(b) $B$ has as many elements as $C$
(c) $A=B \cup C$
(d) $B$ has twice as many elements as $C$
(1981, 2M)
Show Answer
Answer:
Correct Answer: 42.(b)
Solution:
Formula:
Evaluation of the Determinant:
- Since, $A$ is the determinant of order $3$ with entries $0$ or $1$ only.
Also, $B$ is the subset of $A$ consisting of all determinants with value $1$ .
[since, if we interchange any two rows or columns,
then among themself sign changes]
Given, $C$ is the subset having determinant with value $-1$ .
$\therefore B$ has as many elements as $C$.
BETA
