Question

Find X and Y, if X + Y = `[(7, 0),(2, 5)]` and X – Y = `[(3, 0),(0, 3)]`

Answer 1

X + Y = `[(7, 0),(2, 5)]`   ...(i)

X – Y = `[(3, 0),(0, 3)]`   ...(ii)

Adding (i) and (ii), we get: 

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)]`

Subtracting (ii) from (i),

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)]`

Hence, X = `[(5, 0),(1, 4)]`, Y = `[(2, 0),(1, 1)]`.