Chapter 5: Algebra of Matrices

Algebra of Matrices Exercise 5.1 Q1

We know that if a matrix is of the order m × n. It has mm elements. Thus, to find all the possible orders of a matrix having 8 elements, we have to find all the ordered pairs of natural numbers whose products is 8.

This order pairs are (1 ×8), (8 × 1), (2× 4), (4×2)

(1, 5) and (5, 1) are the order pairs of natural number whose product is 5.

Hence, the possible orders of a matrix having 5 element are 1 × 5 and 5 ×1

 

Algebra of Matrices Exercise 5.1 Q2

 

Algebra of Matrices Exercise 5.1 Q3

 

Algebra of Matrices Exercise 5.1 Q4

 

Algebra of Matrices Exercise 5.1 Q5