Question

X तथा Y ज्ञात कीजिए यदि `X + Y = [(7,0),(2,5)]  "तथा"  X - Y = [(3,0),(0,3)]`

Answer 1

`"X" + "Y" = [(7,0),(2,5)]` .... (i)

`"X" - "Y" = [(3,0),(0,3)]` ...... (ii)

समीकरण (i) व (ii), को जोड़ने पर

2x = `[(7, 0),(2, 5)] + [(3, 0),(0, 3)]`

= `[(7 + 3, 0 + 0),(2 + 0, 5 + 3)]`

= `[(10, 0),(2, 8)]`

∴ x = `(1)/(2)[(10, 0),(2, 8)]`

= `[(5, 0),(1, 4)]`

समीकरण (ii) को (i), में से घटाने पर,

2y = `[(7, 0),(2, 5)] - [(3, 0),(0, 3)]`

⇒ 2y = `[(7 - 3, 0 - 0), (2 - 0, 5 - 3)]`

= `[(4, 0), (2, 2)]`

∴ y = `(1)/(2)[(4, 0),(2, 2)]`

= `[(2, 0), (1, 1)]`

अत: `"X" = [(5,0),(1,4)] , "Y" = [(2,0),(1,1)]`