Math Tutoring on Introduction to Matrices
A Matrix is a rectangular arrangement or array of numbers in rows and columns often called elements. The plural of matrix is Matrices. The Size or Dimension (m x n) of a matrix identifies the number of rows as m and the number of columns is n. A matrix having only one row is called a Row Matrix and the matrix having one column is called a Column Matrix.
A matrix in which the number of rows is equal to the number of columns is called a Square Matrix.
A square matrix is called a Diagonal Matrix if no diagonal entries are all zero, the main diagonal can be constants or zeros.
A square matrix in which every diagonal element is 1 and every no diagonal element is 0 is called an Identity Matrix or a Unit Matrix. A matrix in which every element is 0, is called a Zero or Null Matrix.
Two matrices are equal if they have the same dimension and their corresponding elements are equal.
The Transpose of an (n x m) matrix A is an (m x n) matrix written as AT.
There are two ways to form the transpose of a matrix:
1) Write the rows of A as the columns of AT.
2) Write the columns of A as the rows of AT.
If A = [aij] then AT = [aji] .
If A = AT then A is called a Symmetric Matrix.
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1. In (m x p) matrix, between m & p which one represents the row and which one column?
2. How to convert Augmented Matrix to Row Echelon form?
3. What is Diagonal Matrix?
4. How to obtain Transpose of a matrix?
5. How to find free variables from a given matrix?
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