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NCERT Class 12 · Ch 3 Exercise 3.2 · Q10

NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.2 Question 10

Solve for x,y,z,t in 2\(\left[\begin{matrix}x & z\\y & t\end{matrix}\right]\) +3\(\left[\begin{matrix}1 & -1\\0 & 2\end{matrix}\right]\) =3\(\left[\begin{matrix}3 & 5\\4 & 6\end{matrix}\right]\).

💡 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 = \(3\), y = \(6\), z = \(9\), t = \(6\)
  1. Isolate the unknown matrix: \(\left[\begin{matrix}x & z\\y & t\end{matrix}\right]\) = (3/2)(\(\left[\begin{matrix}2 & 6\\4 & 4\end{matrix}\right]\)).
  2. Thus the unknown matrix is \(\left[\begin{matrix}3 & 9\\6 & 6\end{matrix}\right]\). Read x,z from its first row and y,t from its second.

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