Question

What is an equal matrix?

Answer 1

Hint: Two matrices are said to be equal matrices when they have the same order or dimensions and all the corresponding elements are also equal

Complete answer:
If A and B are the matrices of equal order $ m \times n $ and $ {a_{mn}} = {b_{mn}} $ then A and B are called equal Matrices.
 For example, consider the following matrices
 $ A = \left( {\begin{array}{*{20}{c}}
  4&{13} \\
  { - 2}&{19}
\end{array}} \right) $
 $ B = \left( {\begin{array}{*{20}{c}}
  4&{13} \\
  { - 2}&{19}
\end{array}} \right) $
 $ C = \left( {\begin{array}{*{20}{c}}
  4&{13} \\
  {19}&{ - 2}
\end{array}} \right) $
Here, we can clearly notice using the definition of the equal matrices that
 $ A = B;A \ne C;$
Some of the applications of the matrices are-
I.It is a simple and compact method of solving systems of linear equations.
II.It is used as a representation of coefficients in the system of linear equations.
III.It is used in cryptography.
IV.The matrix notation and operations are used in electronic spreadsheet programs for personal computers, which in turn is used in different areas like science and business like sales projection, analysing the results of an experiment, budgeting, etc.
V.It is also used in 3D maths where they are primarily used to describe the relationship between two coordinate spaces.
It also finds use in various branches of science like genetics, sociology, economics, modern psychology and industrial management.

Note: By definition, matrices is an ordered array of numbers (may be real or complex) or functions.
Elements or entries of the matrix are the numbers or the functions in the array.
Rows of the matrices are referred to the horizontal lines of elements.
Columns of the matrix refer to the vertical elements in the matrix.
General format of a matrix is given as $ A = \left( {\begin{array}{*{20}{c}}
  {{a_{11}}}& \ldots &{{a_{1n}}} \\
   \vdots & \ddots & \vdots \\
  {{a_{m1}}}& \cdots &{{a_{mn}}}
\end{array}} \right) $ or $ A = {[{a_{ij}}]_{m \times n}} $
Where, $ 1 \leqslant i \leqslant m,1 \leqslant j \leqslant n $ and $ i,j \in N $
 $ {i^{th}} $ row elements are $ {a_{i1}}\;{a_{i2}}\;{a_{i3}}......{a_{in}} $
 $ {j^{th}} $ row elements are $ {a_{j1}}\;{a_{j2}}\;{a_{j3}}......{a_{mj}} $