A is a singular matrix of order 5. B is anoth | vedclass

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(C) Given that $A$ is a singular matrix of order $5$, its determinant $|A| = 0$. This implies that the rank $\rho(A) < 5$. Since $B$ has a non-zero mi

Vedclass · Accepted Answer

$\rho(A)=\rho(B)=3$, when all the fourth order minors of $A$ are zero

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(C) Given that $A$ is a singular matrix of order $5$, its determinant $|A| = 0$. This implies that the rank $\rho(A) Since $B$ has a non-zero minor of order $3$, the rank $\rho(B) \geq 3$. We are given $\rho(B) = \rho(A)$. If $\rho(A) = 3$, then $\rho(B) = 3$. If $\rho(A) = 4$, then $\rho(B) = 4$. Option $C$ states that $\rho(A) = \rho(B) = 3$ when all fourth-order minors of $A$ are zero. If all fourth-order minors of $A$ are zero, then $\rho(A) \leq 3$. Since $B$ has a non-zero minor of order $3$, $\rho(B) = 3$. Thus, if $\rho(A) = 3$, then $\rho(A) = \rho(B) = 3$ is a consistent statement.

$A$ is a singular matrix of order $5$. $B$ is another matrix having the rank $\rho(B)$ equal to the rank $\rho(A)$, and $B$ has a non-zero minor of order $3$. Then which one of the following is true?

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