## 2.10.4 Matrices, SPM Paper 2 (Long Question)

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

## 2.10.3 Matrices, SPM Paper 2 (Long Questions)

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

## 2.10.2 Matrices, SPM Paper (Long Questions)

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

## 2.10.1 Matrices, SPM Paper (Long Questions)

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 Paper (Short Questions)

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

## 2.9.1 Matrices, SPM Paper (Short Questions)

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

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

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

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

## 2.5.1 Multiplication of Two Matrices (Examples)

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