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Home Questions 44PJ2W2UT9
Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Matrices

Question:

Match List-I with List-II

List-I

List-II

(A) The number of possible matrices of order 3×3 with each entry 1 or 0

(I) $2^4$

(B) The number of possible matrices of order 2×3 with each entry 1 or 0

(II) $2^9$

(C) The number of possible matrices of order 2×3 with each entry 0, 1, 2

(III) $2^6$

(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:

Options:

(A)-(II), (B)-(III), (C)-(IV), (D)-(I)

(A)-(III), (B)-(I), (C)-(IV), (D)-(II)

(A)-(IV), (B)-(I), (C)-(II), (D)-(III)

(A)-(I), (B)-(II), (C)-(III), (D)-(IV)

Correct Answer:

(A)-(II), (B)-(III), (C)-(IV), (D)-(I)

Explanation:

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)

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