Question

The number 3 $\times$ 3 matrices whose entries are either 0 or 1 and for which the system $A\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]$ has exactly two distinct solutions is

• A. 0
• B. $2^9-1$
• C. 168
• D. 2

Answer 1

The correct option is A 0

We know that the system of equations AX=B has either

1. unique solution

2. Infinite number of solutions

3. No solution

In the given system, it tells about 2 distinct solutions.Hence there cannot exist any matrix A such that $A\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]$ has 2 distinct solutions.