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AP EAMCET · Maths · Matrices

If \(A=\left[\begin{array}{ccc}1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6\end{array}\right]\) and the rank of \(A\) is 2, then the value of \(x\) is equal to

  1. A \(1\)
  2. B \(0\)
  3. C \(-3\)
  4. D \(3\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(-3\)

Step-by-step Solution

Detailed explanation

\( \det(A) = 0 \) \( 1((-1)(-6) - (7)(4)) - 2((4)(-6) - (7)(2)) + x((4)(4) - (-1)(2)) = 0 \) \( 1(6 - 28) - 2(-24 - 14) + x(16 + 2) = 0 \) \( -22 - 2(-38) + 18x = 0 \) \( -22 + 76 + 18x = 0 \) \( 54 + 18x = 0 \) \( 18x = -54 \) \( x = -3 \)