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

If $\frac{x^2+7}{(x^2+1)(x-2)}=\frac{A}{x-2}+\frac{Bx+C}{x^2+1}$, then the determinant of the matrix $\begin{bmatrix} A & B \\ C & \frac{2}{5} \end{bmatrix}$ is

If $A=\left[\begin{array}{ccc}2 & 0 & -3 \\ 4 & 3 & 1 \\ -5 & 7 & 2\end{array}\right]$ is expressed as a sum of a symmetric matrix $P$ and a skew-symmetric matrix $Q$,then $P^{T}-Q^{T}=$

Let $\alpha \beta \gamma = 45$; $\alpha, \beta, \gamma \in R$. If $x(\alpha, 1, 2) + y(1, \beta, 2) + z(2, 3, \gamma) = (0, 0, 0)$ for some $x, y, z \in R$ such that $xyz \neq 0$,then $6\alpha + 4\beta + \gamma$ is equal to:

If $A$ is a square matrix of order $3$ with $|A| = 2$,then the value of $|(A - A^T)^5| + |(A^T - A)^3|$ is-

If $M$ and $N$ are square matrices of order $3$, then which one of the following statements is not true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module