## 4.10 Matrices, SPM Paper 2 (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 more4.10 Matrices, SPM Paper 2 (Long Questions)

## 4.8 Solving Simultaneous Linear Equations using Matrices

4.8 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 more4.8 Solving Simultaneous Linear Equations using Matrices

## 4.7 Inverse Matrix

4.7 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 more4.7 Inverse Matrix

## 4.6 Identity Matrix

4.6 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 more4.6 Identity Matrix

## 4.1 Matrices

4.1 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 more4.1 Matrices

## 4.5 Multiplication of Two Matrices

4.5 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 more4.5 Multiplication of Two Matrices

## Matrices Long Questions (Question 4)

Question 4:It is given that   Q( 3 −2 5 −4 )=( 1 0 0 1 ), where Q is a 2 × 2 matrix.(a) Find the matrix Q.(b) Write the following simultaneous linear equations as matrix equation: 3x – 2y = 7 5x – 4y = 9 Hence, using matrix method, calculate the value of x … Read moreMatrices Long Questions (Question 4)

## 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 ) Solution: … Read moreMultiplication of Two Matrices (Examples)