Give the correct order of initials T or F for | vedclass

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Question

(B) Statement $-1$: If two lines are neither parallel nor coincident,they must intersect at exactly one point. Thus,the system has a unique solution.

Vedclass · Accepted Answer

$TTFT$

Vedclass · Answer

(B) Statement $-1$: If two lines are neither parallel nor coincident,they must intersect at exactly one point. Thus,the system has a unique solution. This statement is $T$.Statement $-2$: The system $ax + by = 0$ and $cx + dy = 0$ is a homogeneous system. If it has a non-zero solution,the determinant $ad - bc$ must be $0$. This implies the lines are coincident,leading to infinitely many solutions. This statement is $T$.Statement $-3$: Substitute $x = y$ and $y = 1 + z$ into $x + y + z = 1$. We get $(1 + z) + (1 + z) + z = 1$,which simplifies to $3z + 2 = 1$,so $3z = -1$ or $z = -1/3$. This gives $y = 2/3$ and $x = 2/3$. Since a solution exists,the system is consistent. This statement is $F$.Statement $-4$: If two equations in a system are inconsistent (e.g.,$x + y = 1$ and $x + y = 2$),they cannot be satisfied simultaneously,making the entire system inconsistent. This statement is $T$.The correct order is $TTFT$.

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