Overview:
A matrix is an array of rows and columns that contain numbers or variables. Each position in the matrix is specific and serves a distinct purpose. Matrices can be defined by their size and shape.
How Is A Matrix Defined?
A matrix is defined by the number of rows and columns it has. Those rows and columns are the dimensions of the matrix. A matrix with 2 rows and 3 columns is not the same as a matrix with 3 rows and 2 columns, even if the elements in both matrices are the same. Each element in a matrix is defined by its position within the matrix.
What Are Some Special Matrices?
There are several types of special matrices. A row matrix has all the elements in one row, and a column matrix has all the elements in one column. Square matrices have the same number of elements in rows and columns, such as a 2 X 2 matrix, a 3 X 3 matrix and so on.
When Are Matrices Equal?
One matrix is equal to another only if their dimensions are the same and each element in one matrix is equal to the corresponding element in the other matrix. Suppose one matrix has the elements [2x + y] and another matrix has the elements [10x +3]. The matrices have the same dimensions (in this case, 1 row and 2 columns, also called a row matrix). The element 2x is equal to 10 and the element y is equal to x + 3. One matrix gives more information about another, so that it can be shown that x is equal to 5 and y is equal to 8.
How Are Matrices Used?
There are many applications of matrices, because a matrix is a compact method of encoding information. Matrices are used in computer programming, economics, electronics, and in statistical analysis. Some can even be used to break codes.
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