2.8 Solving Simultaneous Linear Equations using Matrices 1. Two simultaneous linear equations can be written in the matrix equation form. For example, in the simultaneous equations: ax + by = e cx + dy = f can be written in the matrix form as follows: ( a b c d ) ( x y ) = ( e … Read more

2.7 Inverse Matrix 1. If A is a square matrix, B is another square matrix and A × B = B × A = I, then matrix A is the inverse matrix of matrix B and vice versa. Matrix A is called the inverse matrix of B for multiplication and vice versa.   2. The symbol A-1 denotes the inverse matrix … Read more

2.6 Identity Matrix 1. Identity matrix is a square matrix, usually denoted by the letter I and is also known as unit matrix.   2. All the diagonal elements (from top left to bottom right) of an identity matrix are 1 and the rest of the elements are 0. For example, ( 1 0 0 1 )  and  … Read more

Example 1: Find the product of the following pairs of matrices. (a) ( 1   5   2 )( 2 4 3 ) (b) ( 2 8 −3 1 )( 1 0 4 −2 ) (c) ( −3 5 )( 2  6 ) (d) ( 0 4 −1 3 )( 7 −2 ) (e) ( 7  −4 )( −2 0 −1 3 … Read more

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