Let A be the set of all 3 times 3 determinant | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) We know that the interchange of two adjacent rows (or columns) changes the value of a determinant only in sign but not in magnitude.Hence, corresp

Vedclass · Accepted Answer

$n(B)=n(C)$

Vedclass · Answer

(B) We know that the interchange of two adjacent rows (or columns) changes the value of a determinant only in sign but not in magnitude.Hence, corresponding to every element $\Delta \in B$, there is an element $\Delta^{\prime} \in C$ obtained by interchanging two adjacent rows (or columns) in $\Delta$.This implies that $n(B) \leq n(C)$, meaning the number of elements in $B$ is less than or equal to the number of elements in $C$.Similarly, by interchanging two rows in any determinant of $C$, we obtain a determinant in $B$, so $n(C) \leq n(B)$.Therefore, $n(B) = n(C)$, which means $B$ has as many elements as $C$.

Let $A$ be the set of all $3 \times 3$ determinants with entries $0$ or $1$ only and $B$ be the subset of $A$ consisting of all determinants with value $1$. If $C$ is the subset of $A$ consisting of all determinants with value $-1$, then:

Similar Questions

$A=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 1 \\ 0 & 1 & 0\end{array}\right] \Rightarrow A^2-2 A=$

The determinant $\left| \begin{array}{ccc} a^2 & a^2 - (b - c)^2 & bc \\ b^2 & b^2 - (c - a)^2 & ca \\ c^2 & c^2 - (a - b)^2 & ab \end{array} \right|$ is divisible by :

If $A$ is a square matrix such that $A^{2} = A$,then $(I + A)^{3} - 7A$ is equal to

Let $M$ be any $3 \times 3$ matrix with entries from the set $\{0, 1, 2\}$. The maximum number of such matrices,for which the sum of diagonal elements of $M^{T}M$ is $7$,is .............

If $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$ satisfies the equation $x^2 - (a + d)x + k = 0$,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module