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NCERT Class 12 · Ch 3 Miscellaneous Exercise · Q6

NCERT Class 12 Maths · Chapter 3 Matrices · Miscellaneous Exercise Question 6

Find x for which \(\left[\begin{matrix}x & -5 & -1\end{matrix}\right]\)\(\left[\begin{matrix}1 & 0 & 2\\0 & 2 & 1\\2 & 0 & 3\end{matrix}\right]\)\(\left[\begin{matrix}x\\4\\1\end{matrix}\right]\)=0.

💡 Concept Hints

  1. Check the matrix orders and the meaning of the requested operation before calculating.
  2. Keep row and column indices in order. Compare corresponding entries only after the matrix expressions have compatible dimensions.

✅ Step-by-Step Solution

Final Answer: x=±4√3.
  1. The matrix-column product is \(\left[\begin{matrix}x + 2\\9\\2 x + 3\end{matrix}\right]\).
  2. Multiplication by the row gives \(x^{2} - 48\).
  3. Thus x²=48, so x=±4√3. Both values satisfy the original scalar equation.

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