If A = 3 1 - 1 2 , then find f A , where f ( x ) = x 2 - 5 x + 7 .

Given A = 3 1 - 1 2 , f x = x 2 - 5 x + 7 ⇒ f A = A 2 - 5 A + 7 A 2 - 5 A + 7 = A . A - 5 A + 7 I = 3 1 - 1 2 3 1 - 1 2 - 5 3 1 - 1 2 + 7 1 0 0 1 = 3 × 3 + 1 × - 1 3 × 1 + 1 × 2 - 1 × 3 + 2 × - 1 - 1 × 1 + 2 × 2 - 5 × 3 5 × 1 5 × - 1 5 × 2 + 7 × 1 7 × 0 7 × 0 7 × 1 = 9 - 1 3 + 2 - 3 - 2 - 1 + 4 - 15 5 - 5 10 + 7 0 0 7 = 8 - 15 + 7 5 - 5 + 0 - 5 + 5 + 0 3 - 10 + 7 = 0 0 0 0 = 0 So the result is a zero matrix.

Construct a 3 × 2 matrix whose elements are given by a ij = 1 2 [ i − 3 j ] .

In general 3 × 2 matrix is given by A = a 11 a 12 a 21 a 22 a 31 a 32 Now a ij = 1 2 | i - 3 j | , i = 1 , 2 , 3 j = 1 , 2 Therfore a 11 = 1 2 | 1 - 3 × 1 | = 1 , a 12 = 1 2 ∣ 1 - 3 × 21 = 5 2 a 21 = 1 2 2 - 3 × 1 = 1 2 , a 22 = 1 2 ∣ 2 - 3 × 2 I = 2 a 31 = 1 2 | 3 - 3 × 1 | = 0 , a 32 = 1 2 | 3 - 3 × 2 | = 3 2 Hence the required matrix is given by A = 1 5 2 1 2 2 0 3 2

Let A = 2 4 3 2 , B = 1 3 - 2 5 , find 2 A + B .

Given that, A = 2 4 3 2 , B = 1 3 - 2 5 . Consider, 2 A + B = 2 2 4 3 2 + 1 3 - 2 5 = 4 8 6 4 + 1 3 - 2 5 = 5 11 4 9 Thus the value of 2 A + B is 5 11 4 9 .

If A = - 2 4 5 and B = 1 3 - 6 , find ( A B ) '

Given that, the matrices are A = - 2 4 5 and B = 1 3 - 6 Consider, A B = - 2 4 5 1 3 - 6 = - 2 - 6 12 4 12 - 24 5 15 - 30 Now, the transpose of the matrix A B is A B ' = - 2 4 5 - 6 12 15 12 - 24 - 30 .

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Matrices>Haryana Board-2018

Embibe Experts Solutions for Chapter: Matrices, Exercise 1: Haryana Board-2019

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Embibe Experts Mathematics Solutions for Exercise - Embibe Experts Solutions for Chapter: Matrices, Exercise 1: Haryana Board-2019

Attempt the free practice questions on Chapter 3: Matrices, Exercise 1: Haryana Board-2019 with hints and solutions to strengthen your understanding. EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS solutions are prepared by Experienced Embibe Experts.