Matrices, Types of Matrices, Row Matrix, Column Matrix, Square Matrix, Rectangular Matrix

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Types of Matrices

Row Matrix

  • A matrix is said to be a row matrix if it has only one row, but may have any number of columns, e.g. the matrix is a row matrix.

  • The order of a row matrix is .

Column Matrix

  • A matrix is said to be a column matrix if it has only one column, but may have any number of rows, e.g. the matrix is a column matrix.

  • The order of a column matrix is .

Square Matrix

  • A matrix is said to be a square matrix if number of rows is equal to the number of columns, e.g. the matrix having rows and columns is a square matrix.

  • The order of a square matrix is or simply .

  • The diagonal of a square matrix from the top extreme left element to the bottom extreme right element is said to be the principal diagonal. The principal diagonal of the matrix Contains elements and .

Rectangular Matrix

  • A matrix is said to be a rectangular matrix if the number of rows is not equal to the number of columns, e.g. the matrix having rows and columns is a rectangular matrix.

  • It may be noted that a row matrix of order and a column matrix of order are rectangular matrix.

Zero or Null Matrix

  • A matrix each of whose element is zero is called a zero or null matrix, e.g. each of the matrix

  • is a zero matrix. Zero matrix is denoted by .

Diagonal Matrix

  • A square matrix is said to be a diagonal matrix, if all elements other than those occurring in the principal diagonal are zero, i.e., if is a square matrix of order , then it is said to be a diagonal matrix if for all .

  • For example, are diagonal matrices.

Scalar Matrix

A diagonal matrix is said to be a scalar matrix if all the elements in its principal diagonal are equal to some non-zero constant, say e.g., the matrix is a scalar matrix.

Unit or Identity Matrix

A scalar matrix is said to be a unit or identity matrix, if all of its elements in the principal diagonal are unity. It is denoted by , if it is of order e.g., the matrix is a unit matrix of order .

Equal Matrices

Two matrices are said to be equal if they are of the same order and if their corresponding elements are equal.

If is a matrix of order and is a matrix of order , then if

(1) and

(2) for all and

Two matrices and given below are not equal, since they are of different orders, namely and respectively.

Also, the two matrices and are not equal, since some elements of are not equal to the corresponding elements of .

Example:

Determine the values of and , if (a) (b)

Solution:

Since the two matrices are equal, their corresponding elements should be equal.

(a)

(b)

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