JEE Main Algebra — Numbers & Matrices: Matrices and Determinants – Chapter Test

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Difficulty: 10 medium · 10 hard

Matrices and Determinants MCQ questions with answers

The first 3 of 20 questions. Unlock the series for the rest, each with a solution.

1. Q1. If A is a 3×3 matrix satisfying A(adj A) = 10 I, where I is the identity matrix, then |A| equals:

   यदि A एक 3×3 आव्यूह है जो A(adj A) = 10 I को संतुष्ट करता है, जहाँ I तत्समक आव्यूह है, तो |A| बराबर है:

   • A. √10
   • B. 100
   • C. 1000
   • D. 10
   Solution

   The identity A(adj A) = |A| I holds for any square matrix; comparing with A(adj A) = 10 I gives |A| = 10.

   किसी भी वर्ग आव्यूह के लिए तत्समता A(adj A) = |A| I होती है; A(adj A) = 10 I से तुलना करने पर |A| = 10 प्राप्त होता है।

2. Q2. If A is a 3×3 matrix and |adj A| = 16, then |A| equals:

   यदि A एक 3×3 आव्यूह है और |adj A| = 16, तो |A| बराबर है:

   • A. 4
   • B. 16
   • C. ±2
   • D. ±4
   Solution

   For a 3×3 matrix, |adj A| = |A|^(n−1) = |A|², so |A|² = 16 and |A| = ±4.

   किसी 3×3 आव्यूह के लिए, |adj A| = |A|^(n−1) = |A|², अतः |A|² = 16 और |A| = ±4।

3. Q3. The inverse of the matrix [[2, 5], [1, 3]] is:

   आव्यूह [[2, 5], [1, 3]] का व्युत्क्रम है:

   • A. [[2, −5], [−1, 3]]
   • B. [[−3, 5], [1, −2]]
   • C. [[3, −5], [−1, 2]]
   • D. [[3, 5], [1, 2]]
   Solution

   The determinant is 2·3 − 5·1 = 1, so the inverse equals the adjoint [[3, −5], [−1, 2]] divided by 1.

   सारणिक 2·3 − 5·1 = 1 है, अतः व्युत्क्रम सहखंडज [[3, −5], [−1, 2]] को 1 से भाग देने के बराबर है।

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