Define each of the following types of matrices:

(i) null matrix;

Gi) = identity matrix. (2 marks)DICT MOD 1 July 2020

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(i) A null matrix, also known as a zero matrix, is a matrix with all elements equal to zero. It is represented by a matrix of size m x n with all elements equal to zero, where m and n are the number of rows and columns in the matrix, respectively. For example, the matrix

[0 0 0] [0 0 0]

is a 2 x 3 null matrix.

(ii) An identity matrix is a square matrix with 1’s on the main diagonal (top-left to bottom-right) and 0’s everywhere else. It is represented by an m x m matrix with 1’s on the main diagonal and 0’s everywhere else, where m is the size of the matrix. For example, the matrix

[1 0 0] [0 1 0] [0 0 1]

is a 3 x 3 identity matrix. The identity matrix is an important matrix in linear algebra and is often denoted by the symbol I. It has the property that when multiplied by any matrix, the result is the original matrix itself.