A is an m times n matrix of rank 4. If A cont | vedclass

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

Question

(D) Given that $A$ is an $m 	imes n$ matrix of rank $4$. Since $A$ contains an $m$-th order non-singular submatrix, $A$ must be a square matrix of or

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) Given that $A$ is an $m 	imes n$ matrix of rank $4$. Since $A$ contains an $m$-th order non-singular submatrix, $A$ must be a square matrix of order $m 	imes m$. Thus, $n = m$, and the rank of $A$ is $m$. Given that the rank of $A$ is $4$, we have $m = 4$. Also, $A^T A$ is a matrix of order $n 	imes n$. Given that $A^T A$ is a $7 	imes 7$ matrix, we have $n = 7$. However, the condition that $A$ contains an $m$-th order non-singular submatrix implies that $A$ is a square matrix of size $m 	imes m$, which means $m = n$. Re-evaluating the problem statement: If $A^T A$ is $7 	imes 7$, then $n = 7$. If $A$ contains an $m$-th order non-singular submatrix, then $m$ must be equal to the rank of $A$, which is $4$. Therefore, the number of rows $m = 4$.

$A$ is an $m \times n$ matrix of rank $4$. If $A$ contains an $m$-th order non-singular submatrix and $A^T A$ is a $7 \times 7$ matrix, then the number of rows of $A$ is:

Similar Questions

If $A(x) = \left| \begin{array}{ccc} 1 & 2 & 3 \\ x+1 & 2x+1 & 3x+1 \\ x^2+1 & 2x^2+1 & 3x^2+1 \end{array} \right|$, then $\int_0^1 A(x) \, dx$ equals

The rank of the following matrix $A$ is
$A = \begin{bmatrix} 1 & -2 & 3 & -4 \\ 2 & 9 & 4 & 5 \\ 4 & 5 & 10 & -3 \\ 1 & 11 & -1 & 9 \end{bmatrix}$

If $A = [a_{ij}]$,$1 \leq i, j \leq n$ with $n \geq 2$ and $a_{ij} = i + j$ is a matrix,then the rank of $A$ is

If $f(x) = \begin{vmatrix} 2 \cos^4 x & 2 \sin^4 x & 3 + \sin^2 2x \\ 3 + 2 \cos^4 x & 2 \sin^4 x & \sin^2 2x \\ 2 \cos^4 x & 3 + 2 \sin^4 x & \sin^2 2x \end{vmatrix}$,then $\frac{1}{5} f'(0)$ is equal to:

In a matrix $A$,if all the sub-matrices of order $k$ are singular and there is at least one non-singular sub-matrix of order $r$ $(r < k)$,then the rank $(\rho)$ of the matrix $A$:

Vedclass Test Series

Exam Paper Generator

Online Exam Module