if [8(2a+b a-2b 5c-d 4c+3d)] = [8(4 -3 11 24)], then value of a + b − c + 2d is :

(a) 8  (b) 10
(c) 4  (d) −8

This question is inspired from Example 5 - Chapter 3 Class 12   - Matrices

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  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Transcript

Question 8 if [โ– 8(2๐‘Ž+๐‘&๐‘Žโˆ’2๐‘@5๐‘โˆ’๐‘‘&4๐‘+3๐‘‘)] = [โ– 8(4&โˆ’3@11&24)], then value of a + b โˆ’ c + 2d is : (a) 8 (b) 10 (c) 4 (d) โˆ’8 Since matrices are equal. Their corresponding elements are equal 2a + b = 4 5c โ€“ d = 11 a โ€“ 2b = โ€“ 3 4c + 3d = 24 Solving these equations Since matrices are equal. Their corresponding elements are equal 2a + b = 4 5c โ€“ d = 11 a โ€“ 2b = โ€“ 3 4c + 3d = 24 Solving these equations Solving (1) 2a + b = 4 b = 4 โ€“ 2a Putting value of b in (3) a โ€“ 2b = โ€“ 3 Putting b = 4 โ€“ 2a a โ€“ 2(4 โ€“ 2a) = -3 a โ€“ 8 + 4a = -3 a + 4a = -3 + 8 5a = 5 a = 5/5 a = 1 From (1) 2a + b = 4 Putting a = 1 2(1) + b = 4 2 + b = 4 b = 4 โ€“ 2 b = 2 From (2) 5c โ€“ d = 11 5c = 11 + d 5c โ€“ 11 = d d = 5c โ€“ 11 Solving (4) 4c + 3d = 24 Putting d = 5c โ€“ 11 4c + 3(5c โ€“ 11) = 24 4c + 15c โ€“ 33 = 24 19c โ€“ 33 = 24 19c = 24 + 33 19c = 57 c = 57/19 c = 3 Now, d = 5c โ€“ 11 Putting c = 3 d = 5(3) โ€“ 11 d = 15 โ€“ 11 d = 4 Hence, a = 1, b = 2, c = 3 and d = 4 Thus, a + b โˆ’ c + 2d = 1 + 2 โˆ’ 3 + 2(4) = 8 So, the correct answer is (a)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.