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NCERT Class 12 · Ch 4 Exercise 4.1 · Q8

NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.1 Question 8

If \(\left[\begin{matrix}x & 2\\18 & x\end{matrix}\right]\) and \(\left[\begin{matrix}6 & 2\\18 & 6\end{matrix}\right]\) have equal determinants, find x.

💡 Concept Hints

  1. Identify whether this needs determinant expansion, an inverse, or the absolute determinant formula for area.
  2. For a determinant use signed cofactors. For a system first check invertibility; for an area take half the absolute determinant.

✅ Step-by-Step Solution

Final Answer: B: x=±6.
  1. The right determinant is 36−36=0. The left is x²−36.
  2. Thus x²=36. Both x=6 and x=−6 satisfy the equation.

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