Question

what do you mean my the term matrices?name and give examples of all 8 types of matrices

Answer 1

A matrix is a collection of numbers arranged into a fixed number of rows and columns. Usually the numbers are real numbers.
A row matrix is a matrix with only one row.
Example: E is a row matrix of order 1 × 1
Example: B is a row matrix of order 1 × 3

A column matrix is a matrix with only one column.

Example: C is a column matrix of order 1 × 1

A column matrix of order 2 ×1 is also called a vector matrix.

Example: D is a column matrix of order 2 × 1
A zero matrix or a null matrix is a matrix that has all its elements zero.

Example: O is a zero matrix of order 2 × 3
A square matrix is a matrix with an equal number of rows and columns.Example: T is a square matrix of order 2 × 2


Example: V is a square matrix of order 3 × 3


A diagonal matrix is a square matrix that has all its elements zero except for those in the diagonal from top left to bottom right; which is known as the leading diagonal of the matrix.
Example: B is a diagonal matrix.


A scalar matrix is a diagonal matrix where all the diagonal elements are equal. For example:(300030003) (300030003)An upper triangular matrix is a square matrix where all the elements located below the diagonal are zeros. For example:(200310−245) (23−2014005)A lower triangular matrix is a square matrix where all the elements located above the diagonal are zeros. For example:(3−12045001)(300−140251)A unit matrix is a diagonal matrix whose elements in the diagonal are all ones.
Example: P is a unit matrix.
 

Answer 2

A matrix is a way to organize data in columns and rows. A matrix is written inside brackets 
Row Matrix

A row matrix is formed by a single row.



Column Matrix

A column matrix is formed by a single column.



Rectangular Matrix

A rectangular matrix is formed by a different number of rows and columns, and its dimension is noted as: mxn.



Square Matrix

A square matrix is formed by the same number of rows and columns.

The elements of the form aiiconstitute the principal diagonal.

The secondary diagonal is formed by the elements with i+j = n+1.



Zero Matrix

In a zero matrix, all the elements are zeros.



Upper Triangular Matrix

In an upper triangular matrix, the elements located below the diagonal are zeros.



Lower Triangular Matrix

In a lower triangular matrix, the elements above the diagonal are zeros.



Diagonal Matrix

In a diagonal matrix, all the elements above and below the diagonal are zeros.



Scalar Matrix

A scalar matrix is a diagonal matrix in which the diagonal elements are equal.


Identity Matrix

An identity matrix is a diagonal matrix in which the diagonal elements are equal to 1.



Transpose Matrix

Given matrix A, the transpose of matrix A is another matrix where the elements in the columns and rows have switched. In other words, the rows become the columns and the columns become the rows.

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