The number of square matrices of order 5 with | vedclass

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

Question

(B) square matrix of order $5$ where each row sum is $1$ and each column sum is $1$ with entries from $\{0, 1\}$ is a permutation matrix.In the first

Vedclass · Accepted Answer

$120$

Vedclass · Answer

(B) square matrix of order $5$ where each row sum is $1$ and each column sum is $1$ with entries from $\{0, 1\}$ is a permutation matrix.In the first row,there are $5$ possible positions to place the $1$.In the second row,there are $4$ remaining positions available to place the $1$ (since the column used in the first row cannot be used again).In the third row,there are $3$ remaining positions.In the fourth row,there are $2$ remaining positions.In the fifth row,there is only $1$ remaining position.Therefore,the total number of such matrices is $5 	imes 4 	imes 3 	imes 2 	imes 1 = 5! = 120$.

The number of square matrices of order $5$ with entries from the set $\{0, 1\}$,such that the sum of all the elements in each row is $1$ and the sum of all the elements in each column is also $1$,is

Similar Questions

Find $x$ and $y,$ if $2\begin{bmatrix} 1 & 3 \\ 0 & x \end{bmatrix} + \begin{bmatrix} y & 0 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 5 & 6 \\ 1 & 8 \end{bmatrix}$

If $A = \begin{bmatrix} -1 & 0 \\ 0 & 2 \end{bmatrix}$,then $A^3 - A^2$ is equal to

If $A$ and $B$ are symmetric matrices of the same order,then which one of the following is not true?

If $A = \begin{bmatrix} 1 & -2 & 1 \\ 2 & 1 & 3 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & 1 \\ 3 & 2 \\ 1 & 1 \end{bmatrix}$,then $(AB)^T$ is equal to

Assuming that the sums and products given below are defined,which of the following is not true for matrices?

Vedclass Test Series

Exam Paper Generator

Online Exam Module