Q1.7

MCQMarks unknown

Let $Ax = b$ be a system of linear equations where $A$ is an $m \times n$ matrix and $b$ is a $m \times 1$ column vector and $X$ is an $n \times1$ column vector of unknowns. Which of the following is false?

(A)

The system has a solution if and only if, both $A$ and the augmented matrix $[Ab]$ have the same rank.

(B)

If $m < n$ and $b$ is the zero vector, then the system has infinitely many solutions.

(C)

If $m=n$ and $b$ is a non-zero vector, then the system has a unique solution.

(D)

The system will have only a trivial solution when $m=n$ , $b$ is the zero vector and $\text{rank}(A) =n$ .

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