Q39

MCQ2 marks, −0.67

Let $A$ be any $n \times m$ matrix, where $m>n$ . Which of the following statements is/are TRUE about the system of linear equations $Ax=0$ ?

(A)

There exist at least $m-n$ linearly independent solutions to this system

(B)

There exist $m-n$ linearly independent vectors such that every solution is a linear combination of these vectors

(C)

There exists a non-zero solution in which at least $m-n$ variables are $0$

(D)

There exists a solution in which at least $n$ variables are non-zero

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