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NCERT Class 12 · Ch 3 Exercise 3.3 · Q4

NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.3 Question 4

Given Aᵀ=\(\left[\begin{matrix}-2 & 3\\1 & 2\end{matrix}\right]\) and B=\(\left[\begin{matrix}-1 & 0\\1 & 2\end{matrix}\right]\), find (A+2B)ᵀ.

💡 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: \(\left[\begin{matrix}-4 & 5\\1 & 6\end{matrix}\right]\)
  1. Transpose the supplied Aᵀ to obtain A=\(\left[\begin{matrix}-2 & 1\\3 & 2\end{matrix}\right]\).
  2. Then A+2B=\(\left[\begin{matrix}-4 & 1\\5 & 6\end{matrix}\right]\).
  3. Transposing gives \(\left[\begin{matrix}-4 & 5\\1 & 6\end{matrix}\right]\). Alternatively use Aᵀ+2Bᵀ.

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