Question

What are the advantages and disadvantages of matrices?

Answer 1

A matrix is a rectangular representation of numbers (like an array) with rows and columns. It is usually represented with numbers written in square brackets.
\left( {\begin{array}{*{20}{c}} {{a_{11}}}& \ldots &{{a_{1n}}} \\\ \vdots & \ddots & \vdots \\\ {{a_{m1}}}& \cdots &{{a_{mn}}} \end{array}} \right) is a matrix with $m$ rows and $n$ columns.

Complete step by step answer:
A matrix is an array representation of numbers, may be 1 dimensional – with one row or one column, may be 2 dimensional – with rows and columns. A matrix is called a square matrix when the number of rows and columns are equal. Matrices are categorized into different types based on the elements inside the matrix, for example, triangular matrix, diagonal matrix, invertible matrix, singular matrix and so on.
\left( {\begin{array}{*{20}{c}} {{a_{11}}}& \ldots &{{a_{1n}}} \\\ \vdots & \ddots & \vdots \\\ {{a_{m1}}}& \cdots &{{a_{mn}}} \end{array}} \right) is a matrix with $m$ rows and $n$ columns.

The main advantage of matrices is that they can be used to solve polynomial equations.
For example: ${x^5} + 4x + 2 = 0$
The highest power of $x$ is $5$, hence we will go for a square matrix with 5 rows and 5 columns and fill the matrix with the coefficients of the variable and solve the equation.A matrix is very useful in computer science to implement 2 dimensional arrays and 3 dimensional arrays. It is also very useful in vector algebra as well.

The main disadvantage of matrix is that it can not be used to solve equations which have imaginary roots. The arithmetic operations like multiplication become very difficult when it involves matrices. A matrix is not capable of depicting non-linear transformations since they are a linear structure.

Note: To answer this question, we need to know what a matrix is. There are many applications of matrices like where organizations use matrix organizational structure. Every application has advantages as well as disadvantages, if the price we are paying is less than the advantages, we need to go for it. If the price we are paying is too high, then we should go for another alternative.