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NDA 1 2024 Maths, question 1

Topic: Matrices and determinants

Q1

Let AA and BB be matrices of order 3×33\times 3. If ∣A∣=122|A|=\frac{1}{2\sqrt{2}} and ∣B∣=1729|B|=\frac{1}{729}, then what is the value of ∣2B(adj(3A))∣|2B(\text{adj}(3A))| ?

  1. (a) 2727
  2. (b) 2722\frac{27}{2\sqrt{2}}
  3. (c) 272\frac{27}{2}
  4. (d) 11Correct answer

Solution.

Answer: (d) 11

  1. For a 3×3 matrix, det(cA)=c³det A and det(adj A)=(det A)².
  2. Therefore det[2B adj(3A)]=8×(1/729)×[27/(2√2)]²=8×729/(729×8)=1.