Let I denote the 3 times 3 identity matrix an | vedclass

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

Question

(B) The identity matrix $I$ is given by $I = \begin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{bmatrix}$.Rearranging the columns of $I$ results

Vedclass · Accepted Answer

there are six distinct choices for $P$ and $\operatorname{det}(P)=\pm 1$

Vedclass · Answer

(B) The identity matrix $I$ is given by $I = \begin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{bmatrix}$.Rearranging the columns of $I$ results in permutation matrices.For a $3 	imes 3$ matrix, the number of ways to rearrange the $3$ columns is given by $3! = 3 	imes 2 	imes 1 = 6$.Thus, there are $6$ distinct choices for $P$.Since $P$ is a permutation matrix, its determinant is equal to the sign of the permutation, which is either $1$ or $-1$.Therefore, $\operatorname{det}(P) = \pm 1$.Hence, there are six distinct choices for $P$ and $\operatorname{det}(P) = \pm 1$.

Let $I$ denote the $3 \times 3$ identity matrix and $P$ be a matrix obtained by rearranging the columns of $I$. Then,

Similar Questions

If $A^2 = A$,then $(I + A)^3 - 7A =$ . . . . . . ,where $A$ is a square matrix.

If $A = [x \quad y \quad z]$,$B = \begin{bmatrix} a & h & g \\ h & b & f \\ g & f & c \end{bmatrix}$,$C = \begin{bmatrix} x \\ y \\ z \end{bmatrix}$ and $(AB) \cdot C$ is an $m \times n$ order matrix,then:

Let $A$ be a symmetric matrix of order $2$ with integer entries. If the sum of the diagonal elements of $A^{2}$ is $1,$ then the possible number of such matrices is

If $\begin{bmatrix} 2 & -3 \\ 4 & 0 \end{bmatrix} - \begin{bmatrix} a & c \\ b & d \end{bmatrix} = \begin{bmatrix} 1 & 4 \\ 2 & -5 \end{bmatrix}$,then $(a, b, c, d) = $

The order of $[x\,y\,z]\,\,\left[ {\begin{array}{*{20}{c}}a&h&g\\h&b&f\\g&f&c\end{array}} \right]\,\left[ \begin{array}{l}x\\y\\z\end{array} \right]$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module