Matrices

2.5 Multiplication of Two Matrices   1. Two matrices can be multiplied when the number of columns for the first matrix is the same as the number of rows for the second matrix.   For instance, if A is a m × n matrix and B is a n × t matrix, then the product of P … Read more

Example 1: Express the following as single matrix. (a) 3 ( 1 − 4 − 3 2 ) + 2 ( − 3 1 3 − 4 ) (b) 2 ( − 1 0 9 − 4 ) − 4 ( − 2 2 3 − 6 ) − 1 3 ( − 9 − … Read more

2.4 Multiplication of a Matrix by a Number When matrix is multiplied by a number, every element in the matrix is multiplied by the number. Example: Given that  A = ( − 2 4 5 − 6 ) , find each of the following. (a) 3A (b) -2A  Solution: (a) 3 A = 3 ( … Read more

Example 1: Find the addition of the following matrices. (a)( 18   −7 )+( 3        6 ) (b) ( −13 0 7 −1 )+( −1 3 5 6 ) Solution: (a) ( 18   −7 )+( 3       6 ) =( 18+3   −7+6 )=( 21   −1 ) (b) ( −13 0 7 −1 )+( −1 3 5 6 ) … Read more

2.3 Addition and Subtraction of Matrices   (A) Determining whether addition or subtraction can be performed on two given matrices 1. Two matrices can be added or subtracted if both matrices have the same order. 2. The addition or subtraction of two matrices is performed by adding or subtracting the corresponding elements of the matrices. … Read more

Example 1: State the values of the unknowns in the following pairs of equal matrix. ( 1 x + 2 4 − y − 1 ) = ( 1 3 2 − 1 ) Solution: ( 1 x + 2 4 − y − 1 ) = ( 1 3 2 − 1 ) x + … Read more

2.2 Equal Matrices (A) Determining whether two matrices are equal 1. Two matrices are equal if they have the same order and their corresponding elements are equal. For example,  ( a b c d ) = ( e f g h ) Therefore, a = e, b = f, c = g and d = … Read more

2.1 Matrices   A matrix is a rectangular array of numbers enclosed in large brackets. For example ( 2 0 3 1 ) is a matrix .    (A)   Rows, Columns and Order of Matrices 1. A matrix which has m rows and n columns is known as a matrix of order m × n.   2. A row … Read more