Explain the meaning of each of the following types of matrices, giving an example in each case: (i) equal matrices; (ii) row matrix; (iii) transpose matrix; (iv) scalar matrix; (v) square matrix. (10 marks)NOVEMBER 2022

(i) Equal matrices: Two matrices are considered equal if they have the same dimensions (i.e., the same number of rows and columns) and the corresponding elements in each matrix are equal. For example, the following two matrices are equal:

[1 2 3]

[4 5 6]

[1 2 3]

[4 5 6]

(ii) Row matrix: A row matrix is a matrix that has only one row. For example, the following is a row matrix:

[1 2 3]

(iii) Transpose matrix: The transpose of a matrix is a new matrix where the rows and columns of the original matrix are switched. For example, the transpose of the matrix:

[1 2 3]

[4 5 6]

is:

[1 4]

[2 5]

[3 6]

(iv) Scalar matrix: A scalar matrix is a matrix where all elements are equal to a scalar (i.e., a single value). For example, the following is a scalar matrix:

[2 2 2]

[2 2 2]

[2 2 2]

(v) Square matrix: A square matrix is a matrix where the number of rows is equal to the number of columns. For example, the following is a square matrix:

[1 2 3]

[4 5 6]

[7 8 9]

A square matrix of n x n is called n-square matrix.