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NCERT Class 12 · Ch 4 Exercise 4.1 · Q7

NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.1 Question 7

Find x: (i) \(\left[\begin{matrix}2 & 4\\5 & 1\end{matrix}\right]\) and \(\left[\begin{matrix}2 x & 4\\6 & x\end{matrix}\right]\) have equal determinants; (ii) \(\left[\begin{matrix}2 & 3\\4 & 5\end{matrix}\right]\) and \(\left[\begin{matrix}x & 3\\2 x & 5\end{matrix}\right]\) have equal determinants.

💡 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: (i) x=±√3; (ii) x=2.
  1. (i) The left determinant is 2−20=−18. The right is 2x²−24.
  2. Thus 2x²−24=−18, so x²=3 and x=±√3. Both signs satisfy the original equality.
  3. (ii) The left determinant is 10−12=−2; the right is 5x−6x=−x.
  4. Hence −x=−2 and x=2.

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