Let and be matrices of orders and respectively

MATHEMATICS · Subjective · CBSE · Mathematics · Matrices · Matrices

Problem

Let

A,\,B,\,C

and

D

be matrices of orders

4\times 3,\,3\times 2,\,2\times 4

and

4\times 4

respectively. (a) For each of the following single products, state with reason whether it is defined and, if so, give the order of the result:

AB,\;AC,\;AD,\;BA,\;BD,\;CB,\;CD,\;DC

. (b) List all products of two matrices among

A,\,B,\,C,\,D

whose result is of order

4\times 4

. (c) Decide which of the following sums can be carried out. Whenever a sum is possible, give the common order of the addends: (i)

AB + D

(ii)

AC + C

(iii)

BD + DC

(iv)

CB + AB