jee-advanced 2010 Q33

jee-advanced · India · paper1 Matrices Linear System and Inverse Existence

The number of $3 \times 3$ matrices A whose entries are either 0 or 1 and for which the system $A \left[ \begin{array} { l } x \\ y \\ z \end{array} \right] = \left[ \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right]$ has exactly two distinct solutions, is
A) 0
B) $2 ^ { 9 } - 1$
C) 168
D) 2

The number of $3 \times 3$ matrices A whose entries are either 0 or 1 and for which the system $A \left[ \begin{array} { l } x \\ y \\ z \end{array} \right] = \left[ \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right]$ has exactly two distinct solutions, is\\
A) 0\\
B) $2 ^ { 9 } - 1$\\
C) 168\\
D) 2

Paper Questions

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