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JEE Advanced 2008Paper 1
Exam
JEE Advanced
Year
2008
Paper
Paper 1
Subject
Mathematics
Chapter
Determinants

JEE Advanced 2008 · Paper 1 · Mathematics · Determinants

Consider the system of equations x-2 y+3 z=-1, x-3 y+4 z=1 and...

Consider the system of equations x−2y+3z=−1,x−3y+4z=1and−x+y−2z=kx-2 y+3 z=-1, x-3 y+4 z=1 and -x+y-2 z=k Statement 1 The system of equations has no solution for k≠3k \neq 3. Statement 2 The determinant \left|13−1−1−2k141\begin{array}{ccc}1 & 3 & -1 \\ -1 & -2 & k \\ 1 & 4 & 1\end{array}$\right| \neq 0, for k≠3k \neq 3.$Consider the system of equations x-2 y+3 z=-1, x-3 y+4 z=1 and -x+y-2 z=k Statement 1 The system of equations has noConsider the system of equations x-2 y+3 z=-1, x-3 y+4 z=1 and -x+y-2 z=k Statement 1 The system of equations has no

Options

  1. AStatement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
  2. BStatement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
  3. CStatement 1 is true, Statement 2 is false.
  4. DStatement 1 is false, Statement 2 is true

Correct answer

A. Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.

Step-by-step solution

 The given system of equations can be expressed as \text{ The given system of equations can be expressed as } Consider the system of equations x-2 y+3 z=-1, x-3 y+4 z=1 and -x+y-2 z=k Statement 1 The system of equations has no
When k≠3k \neq 3, the given system of equations has no solution. ⇒\Rightarrow Statement 1 is true.Clearly, Statement 2 is also true as it is rearrangement of rows and columns ofConsider the system of equations x-2 y+3 z=-1, x-3 y+4 z=1 and -x+y-2 z=k Statement 1 The system of equations has no
Hence, option (a) is correct.
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