Question

Find X and Y, if 2X + 3Y = `[(2, 3),(4, 0)]` and 3X + 2Y = `[(2, -2),(-1, 5)]`

Answer 1

2X + 3Y = `[(2, 3),(4, 0)]`   ...(i)

3X + 2Y = `[(2, -2),(-1, 5)]`   ...(ii)

Subtracting equation (i) by 3 and (ii) by 2,

3(2X + 3Y) – 2(3X + 2Y)

= `3[(2, 3),(4, 0)] - 2[(2, -2),(-1, 5)]`

⇒ 6X + 9Y – 6X – 4Y

= `[(6, 9),(12, 0)] - [(4, -4),(-2, 10)]`

⇒ 5Y = `[(2, 13),(14, -10)]`

⇒ Y = `[(2/5,13/5),(14/5,-2)]`

Again, subtracting equation (i) multiplied by 2 and (ii) by 3,

2(2x + 3y) – 3(3x – 2y)

= `2[(2, 3),(4, 0)] - 3[(2, -2),(-2, 5)]`

4X – 9Y = `[(4, 6),(8, 0)] - [(6, -6),(-3, 15)]`

–5X = `[(-2, 12),(11, -15)]`

X = `-1/5 [(-2, 12),(11, -15)]`

= `[(2/5, -12/5),(-11/5, 3)]`

Hence, X = `[(2/5, -12/5),(-11/5, 3)]`, Y = `[(2/5, 13/5),(14/5, -2)]`