A is a $3 \times 4$ matrix and $A X = B$ is an inconsistent system of equations. The highest possible rank of A is

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Solution

The correct option is B 2
Given A is a $3 \times 4$ matrix
So [A : B] is $3 \times 5$ matrix
$ρ (A) \leq 3 a n d ρ (A : B) \leq 3$ .
But AX = B is an inconsistent system
$\Rightarrow ρ (A) \neq ρ (A : B)$ .
$Hence, only possiblility is that ρ (A) < ρ (A : B)$
$\Rightarrow m a x ρ (A) = 2$ & $m a x ρ (A : B) = 3$

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A is a 3×4 matrix and AX=B is an inconsistent system of equations. The highest possible rank of A is

The correct option is B 2Given A is a 3×4 matrix So [A : B] is 3×5 matrix ρ(A)≤3andρ(A:B)≤3. But AX = B is an inconsistent system ⇒ ρ(A)≠ρ(A:B). Hence, only possiblility is that ρ(A)<ρ(A:B) ⇒maxρ(A)=2 & maxρ(A:B)=3

A is a $3 \times 4$ matrix and $A X = B$ is an inconsistent system of equations. The highest possible rank of A is