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JEE Advanced 2010Paper 1
Exam
JEE Advanced
Year
2010
Paper
Paper 1
Subject
Mathematics
Chapter
Matrices

JEE Advanced 2010 · Paper 1 · Mathematics · Matrices

The number of 3 × 3 matrices A whose entries are either 0 or 1 and...

The number of 3×33 \times 3 matrices AA whose entries are either 0 or 1 and for which the system AA\left[xyz\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[100\begin{array}{l}1 \\ 0 \\ 0\end{array}\right] has exactly two distinct solutions, is

Options

  1. A0
  2. B29−12^9-1
  3. C168
  4. D2

Correct answer

A. 0

Step-by-step solution

Since, AA\left[xyz\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[100\begin{array}{l}1 \\ 0 \\ 0\end{array}\right] 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, number of matrices AA is zero.
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