# Further Mathematics - Exam Revision

## The inverse of a matrix

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Why inverse matrices? The inverse of a matrix is also called the reciprocal of the matrix. Since matrices cannot be divided, inverse matrices are used as the reciprocal operation of multiplication of matrices. Notation If A is a square matrix, then its inverse is also a square matrix and it is denoted by A−1. AA−1 = I, where I is the identity matrix. For example, in the equation AX = B, where A, X and B are matrices, X = A−1B. Invertible matrices must be square matrices (the number of rows equals the number of columns). Here are some square matrices: (2 × 2) (3 × 3)  (4 × 4)   ...

## Operations with Matrices

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Addition and subtraction of matrices Requirement: Matrices must be of the same order. How to: Corresponding elements are added (in addition) or subtracted (in subtraction). Example Consider the two matrices given below.                 a. Calculate the matrix A + B.     The two matrices are of the same order, (2 × 3),  so they can be added.   b. Calculate the matrix A − B.     The two matrices are of the same order, (2 × 3),  so they can be subtracted.   Multiplying a matrix by a scalar A scalar is any real number. When multiplying a matrix...

## Matrices ... What are they?

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## Part 1 - Further Mathematics - Unit 3 - DATA ANALYSIS - Types of data

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## Population, samples and simple random sampling

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POPULATIONS AND SAMPLES A population consists of all members (people, objects or events) of a specified group about which information is sought. Examples all the teenagers in a country; all the students in a school; all the kangaroos in Australia.   A sample is a representative subset of the population and it consists of some members (people, objects or events) of the population that we collect to make inferences. Examples a group of teenagers in a country; a group of students in a school; a group of kangaroos in Australia.   If the sample is random and large enough, the information collected from the sample can be used to make inferences about the population....

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