## A matrix is said to be a column matrix if it has only one column. (iii) A matrix in which the number of rows are equal to the num

Question

A matrix is said to be a column matrix if it has only one column.

(iii) A matrix in which the number of rows are equal to the number of columns,

is said to be a square matrix. Thus, an m × n matrix is said to be a square

matrix if m = n and is known as a square matrix of order ‘n’.

(iv) A square matrix B = [bij]

n×n

is said to be a diagonal matrix if its all non

diagonal elements are zero, that is a matrix B = [bij]

n×n

is said to be a

diagonal matrix if bij = 0, when i ≠ j.

(v) A diagonal matrix is said to be a scalar matrix if its diagonal elements are

equal, that is, a square matrix B = [bij]

n×n

is said to be a scalar matrix if

bij = 0, when i ≠ j

bij = k, when i = j, for some constant k. (vi) A square matrix in which elements in the diagonal are all 1 and rest are

all zeroes is called an identity matrix.

In other words, the square matrix A = [aij]

n×n

is an identity matrix, if

aij = 1, when i = j and aij = 0, when i ≠ j. (vii) A matrix is said to be zero matrix or null matrix if all its elements are

zeroes. We denote zero matrix by O.

(ix) Two matrices A = [aij] and B = [bij] are said to be equal if

(a) they are of the same order, and

(b) each element of A is equal to the corresponding element of B, that is,

aij = bij for all i and j.​

in progress 0
1 month 2021-10-22T02:05:14+00:00 2 Answers 0 views 0