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NCERT Class 12 · Ch 3 Exercise 3.1 · Q7

NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.1 Question 7

Find a,b,c,d if \(\left[\begin{matrix}a - b & 2 a + c\\2 a - b & 3 c + d\end{matrix}\right]\) = \(\left[\begin{matrix}-1 & 5\\0 & 13\end{matrix}\right]\).

💡 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: a = \(1\), b = \(2\), c = \(3\), d = \(4\)
  1. Equate entries: a−b=−1, 2a+c=5, 2a−b=0, 3c+d=13.
  2. Subtract the first equation from the third to obtain a=1. Then b=2,c=3,d=4.
  3. Substitution gives the required right-hand matrix.

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