Let A be a 3 times 3 matrix with operatorname | vedclass

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

Question

(D) Given that $A$ is a $3 	imes 3$ matrix and $\operatorname{det}(A) = 4$.First,consider the matrix $2A$. Since $A$ is a $3 	imes 3$ matrix,$\opera

Vedclass · Accepted Answer

$64$

Vedclass · Answer

(D) Given that $A$ is a $3 	imes 3$ matrix and $\operatorname{det}(A) = 4$.First,consider the matrix $2A$. Since $A$ is a $3 	imes 3$ matrix,$\operatorname{det}(2A) = 2^{3} 	imes \operatorname{det}(A) = 8 	imes 4 = 32$.Next,the matrix $B$ is obtained from $2A$ by the row operation $R_{2} ightarrow 2R_{2} + 5R_{3}$.Applying the property of determinants,if a row is multiplied by a scalar $k$,the determinant is multiplied by $k$. Here,$R_{2}$ is replaced by $2R_{2} + 5R_{3}$.This operation is equivalent to multiplying the second row by $2$ and then adding $5$ times the third row to it. Adding a multiple of one row to another does not change the value of the determinant.Therefore,$\operatorname{det}(B) = 2 	imes \operatorname{det}(2A) = 2 	imes 32 = 64$.

Let $A$ be a $3 \times 3$ matrix with $\operatorname{det}(A) = 4$. Let $R_{i}$ denote the $i^{\text{th}}$ row of $A$. If a matrix $B$ is obtained by performing the operation $R_{2} \rightarrow 2R_{2} + 5R_{3}$ on $2A$,then $\operatorname{det}(B)$ is equal to:

Similar Questions

Without expanding,prove that $\Delta = \begin{vmatrix} x+y & y+z & z+x \\ z & x & y \\ 1 & 1 & 1 \end{vmatrix} = 0$.

If $\left| \begin{array}{ccc} -2a & a+b & a+c \\ b+a & -2b & b+c \\ c+a & b+c & -2c \end{array} \right| = \alpha (a+b)(b+c)(c+a) \neq 0$,then $\alpha$ is equal to

If $x, y$ and $z$ are greater than $1$,then the value of $\left|\begin{array}{ccc}1 & \log _{x} y & \log _{x} z \\ \log _{y} x & 1 & \log _{y} z \\ \log _{z} x & \log _{z} y & 1\end{array}\right|$ is

If $\left| \begin{array}{ccc} y + z & x & y \\ z + x & z & x \\ x + y & y & z \end{array} \right| = k(x + y + z)(x - z)^2$,then $k = $

$A$ value of $\theta \in (0, \pi /3)$,for which $\left| \begin{array}{ccc} 1 + \cos^2 \theta & \sin^2 \theta & 4 \cos 6\theta \\ \cos^2 \theta & 1 + \sin^2 \theta & 4 \cos 6\theta \\ \cos^2 \theta & \sin^2 \theta & 1 + 4 \cos 6\theta \end{array} \right| = 0$,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module