Question

The number of $3 \times 3$ matrices $A$ whose entries are either $0$ or $1$ and for which the system A $\begin {bmatrix} x \\\ y \\\ z \end {bmatrix}-\begin {bmatrix} 1 \\\ 0 \\\ 0 \end {bmatrix}$ has exactly two distinct solutions, is

• A. 0
• B. $2^9 -1$
• C. 168
• D. 2

Answer 1

Answer: (A)

0

Answer 2

Since, A$\begin {bmatrix} x \\\ y \\\ z \end {bmatrix}-\begin {bmatrix} 1 \\\ 0 \\\ 0 \end {bmatrix}$ is linear equation in three variables and that could have only unique, no solution or infinitely many solution.
$\therefore \$ It is not possible to have two solutions.
Hence, num ber of matrices A is zero