Matrices definition

According to the matrices definition, a matrix can be considered as a multi-dimensional array of rectangular form consisting of real numbers or expressions. All this numbers are arranged in rows and columns and are known as matrix elements. Before proceeding to the examples of matrices, we will have a look at its history and methods for solving matrices.

A look at the history of matrices:

The history of matrices goes long back to ancient ages. The matrices came in life as a solution to system of linear equations. Thanks to Babylonians who started solving this equations and came up with matrice. It followed many derivations and eventually began to be used in various fields.

Important points for solving matrices:


A generalized
matrice math is shown below. As shown, it could be of any dimensions. The important points are listed out according to the matrice definition.
matrices

  • The matrices of same rows and columns can be added/subtracted entry by entry i.e. each matrix element has to be processed with corresponding element from another matrix.

  • Any two matrix can be multiplied if and only if the columns in first one is equal to the rows in the second one.

  • The inverse of square matrix exists if and only if determinant value is non-zero.

  • The commutative and associative properties holds true for addition of matrices.

  • A constant can be multiplied with any matrix.

This properties help a lot in solving matrices problems. So lets move on to matrices examples thereby having a grip on the topic.

Solving some matrices examples:

Some examples are given below for the practice purpose. This will give you a proper idea of matrix and help solving future problems.

(1) Consider A is a random matrix. What would you get if you multiply it with identity matrix?
Identity matrix is the one which has all the diagonal elements as 1 and the rest are all zeroes. We have a property A x I = A where I is the identity matrix. Hence the answer would be matrix itself.

(2) Consider matrices formula 

Find sum of A and B: 
We know that if we want to add two matrix, we need to add each respective elements. Lets consider output as C. Then we have

matrices problems

The computer programmers have to deal with matrices in their daily life in the form of arrays of multi dimensions. 

Video lesson on Matrices Solving Systems

More topics in Matrices
Matrices Matrix Multiplication
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