jee-advanced 2009 Q35

jee-advanced · India · paper1 Matrices Linear System and Inverse Existence
Let $\mathscr { A }$ be the set of all $3 \times 3$ symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0.
The number of matrices $A$ in $\mathscr { A }$ for which the system of linear equations
$$A \left[ \begin{array} { l } x \\ y \\ z \end{array} \right] = \left[ \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right]$$
is inconsistent, is
(A) 0
(B) more than 2
(C) 2
(D) 1
Let $\mathscr { A }$ be the set of all $3 \times 3$ symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0.

The number of matrices $A$ in $\mathscr { A }$ for which the system of linear equations

$$A \left[ \begin{array} { l } x \\ y \\ z \end{array} \right] = \left[ \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right]$$

is inconsistent, is\\
(A) 0\\
(B) more than 2\\
(C) 2\\
(D) 1