cmi-entrance 2014 Q4

cmi-entrance · India · pgmath 4 marks Not Maths
Let $A \in M_{m \times n}(\mathbb{R})$ and let $b_0 \in \mathbb{R}^m$. Suppose the system of equations $Ax = b_0$ has a unique solution. Which of the following statement(s) is/are true?
(A) $Ax = b$ has a solution for every $b \in \mathbb{R}^m$.
(B) If $Ax = b$ has a solution then it is unique.
(C) $Ax = 0$ has a unique solution.
(D) $A$ has rank $m$.
Let $A \in M_{m \times n}(\mathbb{R})$ and let $b_0 \in \mathbb{R}^m$. Suppose the system of equations $Ax = b_0$ has a unique solution. Which of the following statement(s) is/are true?\\
(A) $Ax = b$ has a solution for every $b \in \mathbb{R}^m$.\\
(B) If $Ax = b$ has a solution then it is unique.\\
(C) $Ax = 0$ has a unique solution.\\
(D) $A$ has rank $m$.