Q23

MCQ2 marks, −0.5

$F$ is an $n\times n$ real matrix. $b$ is an $n\times 1$ real vector. Suppose there are two $n\times 1$ vectors, $u$ and $v$ such that, $u ≠ v$ and $Fu = b, Fv = b$ . Which one of the following statements is false?

(A)

Determinant of $F$ is zero.

(B)

There are an infinite number of solutions to $Fx = b$

(C)

There is an $x≠0$ such that $Fx = 0$

(D)

$F$ must have two identical rows

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