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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.
Solution
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
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