Definition 2 Two matrices A a and B b are said to be equal if i they are of the same order ii each element of A is equal to the corresponding element of B that is a all i and j 3 For example 2 and 2 1 not equal matrices Symbolically if two matrices A and B are equal we write A B X y 1 5 0 If z a 2 b C 3 Example 4 If x 3 42 Simplifying we get 6 then 2 6 a 1 b 3 21 z 4 2y 7 MATHEMATICS 0 2 are equal matrices but Free 5 Find the values of a b c x y and z Solution As the given matrices are equal therefore their corresponding elements must be equal Comparing the corresponding elements we get x 3 0 z 4 6 2y 7 3y 2 a 1 3 b 3 2b 4 Solving these equations we get 1 In the matrix A 35 2 0 2c 2 a 2 b 7 c 1 x 3 y 5 z 2 Example 5 Find the values of a b c and d from the following equation 2a b a 2b 4 3 H 5c d 4c 3d 24 6 2b 4 21 0 6 3y 2 3 2c 2 Rationalised 2023 24 a 1 b 2 c 3 and d 4 19 5 Solution By equality of two matrices equating the corresponding elements we get 5c d 11 2a b 4 a 2b 3 4c 3d 24 EXERCISE 3 1 12 3 2 1 a 6 b 3 c 2 17 and write b for 3 1 5 i The order of the matrix ii The number of ele iii Write the elements a13 a21 9332 A242 23 2 If a matrix has 24 elements what are the possible has 13 elements are ned it can have What if it 3 If a matrix has 18 elements what are the possible orders it can have What if it hata