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NCERT Class 12 · Ch 3 Exercise 3.2 · Q12

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

Find x,y,z,w if 3\(\left[\begin{matrix}x & y\\z & w\end{matrix}\right]\) = \(\left[\begin{matrix}x & 6\\-1 & 2 w\end{matrix}\right]\) + \(\left[\begin{matrix}4 & x + y\\w + z & 3\end{matrix}\right]\).

💡 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 = \(2\), y = \(4\), z = \(1\), w = \(3\)
  1. The entries give 2x=4, 2y=x+6, 2z=w−1 and w=3.
  2. Solve in this order: x=2,y=4,w=3,z=1. Substitute to verify all four entries.

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