O. Its order will be clear from the context. . .
Equality of matrices Definition Two matrices A = [ a ij ] and B = [ b ij ] are said to be equal if they are of the same order each element of A is equal to the corresponding element of B, that is a ij = b ij for all i and j . For example, are equal matrices but are not equal matrices. Symbolically, if two matrices A and B are equal, we write A = B. If .
z = , then x = – . , y = , z = , a = , b = , c = Example If z 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 + = , z + = , y – = y – a – = – , = c + b – = b + , Simplifying, we get a = – , b = – , c = – , x = – , y = – , z = Example Find the values of a , b , c , and d from the following equation: d d Solution By equality of two matrices, equating the corresponding elements, we get a + b = c – d = a – b = – c + d = Solving these equations, we get a = , b = , c = and d = EXERCISE .
. In the matrix , write: (i) The order of the matrix, (ii) The number of elements, (iii) Write the elements a , a , a , a , a . . If a matrix