Matrices

Question 10:It is given that matrix M is a 2 × 2 matrix such that M( −2   1 1      3 )=( 1    0 0    1 ) (a) Find matrix M. (b)   Write the following simultaneous linear equations as matrix equations: –2x + y = 10 x + 3y = 9       Hence, using matrix method, calculate the value of x and of … Read more

Question 8:The inverse matrix of   ( 4 −1 2 5 ) is t( 5 1 −2 n ). (a) Find the value of n and of t.(b) Write the following simultaneous linear equations as matrix equation:4x – y = 72x + 5y = –2Hence, using matrix method, calculate the value of x and of y.Solution: (a) t( 5 1 −2 n )= ( … Read more

Question 5: (a) Given  1 14 ( 2 s −4 t )( t −1 4 2 )=( 1 0 0 1 ), find the value of s and of t. (b) Write the following simultaneous linear equations as matrix form: 3x – 2y = 5 9x + y = 1 Hence, using matrix method, calculate the value of x and y. Solution: (a) 1 … Read more

Question 1: It is given that matrix A = ( 3 − 1 5 − 2 ) (a) Find the inverse matrix of A. (b) Write the following simultaneous linear equations as matrix equation: 3u – v = 9 5u – 2v = 13 Hence, using matrix method, calculate the value of u and v. … Read more

2.9.2 Matrices, SPM Practice (Short Questions) Question 5: Given that ( 3   x ) ( x − 1 ) = ( 18 ) ,  find the value of x. Solution: ( 3   x ) ( x − 1 ) = ( 18 ) [3 × x + x (–1)] = (18) 3x – … Read more

Question 1: ( 1 4 6 2 ) + 3 ( 2 0 4 − 3 ) − ( − 3 0 − 2 − 5 ) Solution: ( 1 4 6 2 ) + 3 ( 2 0 4 − 3 ) − ( − 3 0 − 2 − 5 ) = ( … Read more

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