The number of 3 × 3 matrices A whose entries are either 0 or 1 and for which the system A\left[\right. x \\ y \\ z \left]\right. = \left[\right. 1 \\ 0 \\ 0 \left]\right. has exactly two distinct solutions, is

Engineering

Mathematics

Solving System of Linear Equation Cramers Rule

Question

The number of 3 × 3 matrices A whose entries are either 0 or 1 and for which the system

A $[\begin{matrix} x \\ y \\ z \end{matrix}] = [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}]$ has exactly two distinct solutions, is

168

2⁹ – 1

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No such matrix is possible as 3 distinct plane cannot have exactly two solutions.

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