Question

If A = `|("p","q"),(8,5)|` , B = `|(3"p",5"q"),(2"q" , 7)|` and if A + B = `|(12,6),(2"r" , 3"s")|` , find the values of p,q,r and s.

Answer 1

A = `|("p","q"),(8,5)|_(2 xx 2)`  , B = `|(3"p",5"q"),(2"q" , 7)|_(2 xx 2)`

A + B = `|("p" + 3"q" , "q" + 5"q"),(8 + 2"q" ,5 + 7)|`

A + B = `|(4"p" , 6"q"),(8 + 2"q" , 12)|_(2 xx 2)`  ..............(1)

But given , A + B = `|(12,6),(2"r" , 3"s")|_(2 xx 2)`  ...............(2)

From (1) and (2)

`|(4"p" , 6"q"),(8 + 2"q" , 12)|` = `|(12,6),(2"r" , 3"s")|`

4p = 12

⇒ p = 3

6q = 6

c q = 1

8 + 2q = 2 r

8 + 2 = 2r

⇒ r = 5

12 = 3s

⇒ s = 4