Match List-I with List-II
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List-I |
List-II |
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(A) The number of possible matrices of order 3×3 with each entry 1 or 0 |
(I) $2^4$ |
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(B) The number of possible matrices of order 2×3 with each entry 1 or 0 |
(II) $2^9$ |
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(C) The number of possible matrices of order 2×3 with each entry 0, 1, 2 |
(III) $2^6$ |
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(D) The number of possible matrices of order 2×2 with each entry 1 or 0 |
(IV) $3^6$ |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
Each entry of a matrix can independently take a given number of values. So, the total number of such matrices is the number of choices per entry raised to the power of total number of entries.
(A) For a 3×3 matrix with each entry either 0 or 1: total entries = 9, choices = 2
Total = $2^9$ → (II)
(B) For a 2×3 matrix with entries 0 or 1: total entries = 6
Total = $2^6$ → (III)
(C) For a 2×3 matrix with entries 0, 1, or 2: choices = 3, entries = 6
Total = $3^6$ → (IV)
(D) For a 2×2 matrix with entries 0 or 1: entries = 4
Total = $2^4$ → (I)