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Matrices and Determinants question

2012 · Shift 2 · Q36
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  5. /2012 · Shift 2 · Q36

Matrices and Determinants question

2012 · Shift 2 · Q36

JEE AdvancedMathematicsMatrices and DeterminantsMCQ+3 / −1
If P is a 3 ×\times× 3 matrix such that PT = 2P + I, where PT is the transpose of P and I is the 3 ×\times× 3 identity matrix, then there exists a column matrix X=[xyz]e[000]X = \left[ {\begin{matrix} x \\ y \\ z \\ \end{matrix} } \right] e \left[ {\begin{matrix} 0 \\ 0 \\ 0 \\ \end{matrix} } \right]X=​xyz​​e​000​​ such that
  1. A
    PX=[000]PX = \left[ {\begin{matrix} 0 \\ 0 \\ 0 \\ \end{matrix} } \right]PX=​000​​
  2. B
    PX = X
  3. C
    PX = 2X
  4. D
    PX = −-− X
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