TOPICS

Miscellaneous

Matrices

**Question-1 :-**

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**Question-4 :-**

**Question-5 :-**

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**Question-7 :-**

**Question-8 :-**

(i)

(ii)

**Question-9 :-**

**Question-10 :-**

**Question-11 :-**
Using properties of determinants, prove that:

**Question-12 :-**
Using properties of determinants, prove that:

**Question-13 :-**
Using properties of determinants, prove that:

**Question-14 :-**
Using properties of determinants, prove that:

**Question-15 :-**
Using properties of determinants, prove that:

**Question-16 :-**
Solve the system of equations:

Let 1/x = a, 1/y = b, 1/z = c 2a + 3b + 10c = 4 4a – 6b + 5c = 1 6a + 9b – 20c = 2 a = 1/2; x = 2 b = 1/3; y = 3 c = 1/5; z = 5

**Question-17 :-**
If a, b, c, are in A.P, then the determinant
(A) 0 (B) 1 (C) x (D) 2x

The correct answer is A.

**Question-18 :-**

The correct answer is A.

**Question-19 :-**
(A) Det(A) = 0 (B) Det(A) ∈ (2, ∞) (C) Det(A) ∈ (2, 4) (D) Det(A) ∈ [2, 4]

|A| = 1(1 + sin²θ) - sin θ(-sin θ + sin θ) + 1(sin²θ + 1) = 1 + sin²θ + sin²θ + 1 = 2 + 2sin²θ = 2(1 + sin²θ) Now, 0 ≤ θ ≤ 2π 0 ≤ sin θ ≤ 1 0 ≤ sin²θ ≤ 1 1 ≤ 1+sin²θ ≤ 2 2 ≤ 2(1+sin²θ) ≤ 4 Det(A) ∈ [2, 4] The correct answer is D.

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