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

Find $AB,$ if $A=\left[\begin{array}{ll}6 & 9 \\ 2 & 3\end{array}\right]$ and $B=\left[\begin{array}{lll}2 & 6 & 0 \\ 7 & 9 & 8\end{array}\right].$

For what values of $x$: $\left[\begin{array}{lll}1 & 2 & 1\end{array}\right]\left[\begin{array}{lll}1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2\end{array}\right]\left[\begin{array}{l}0 \\ 2 \\ x\end{array}\right]=O$?

If $A = \begin{bmatrix} 1 & 4 & 4 \\ 4 & 1 & 4 \\ 4 & 4 & 1 \end{bmatrix}$,then $A^2 - 6A =$ . . . . . . (in $I_3$)

If $A^2 = A$ is a square matrix such that $(I - A)^n = I - A$ for $n \geq 1$,then what is the value of $(I + A)^2 - 3A$?

If $[m \ n] \begin{bmatrix} m \\ n \end{bmatrix} = [25]$ and $m < n$,then $(m, n) =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module