# Solve the following equations for X and Y, if 3X − Y = [1-1-11] and X – 3Y = [0-10-1]. - Mathematics and Statistics

Sum

Solve the following equations for X and Y, if 3X − Y = [(1, -1),(-1, 1)]  and X – 3Y = [(0, -1),(0, -1)].

#### Solution

Given equations are

3X – Y = [(1, -1),(-1, 1)]          ...(i)

and X – 3Y = [(0, -1),(0, -1)]     ...(ii)

By (i) x 3 – (ii), we get

8X = 3[(1, -1),(-1, 1)] - [(0, -1),(0, -1)]

= [(3, -3),(-3, 3)] - [(0, -1),(0, -1)]

= [(3 - 0, -3 + 1),(-3 - 0, 3 + 1)]

∴ 8X = [(3, -2),(-3, 4)]

∴ X = (1)/(8) [(3, -2),(-3, 4)]

∴ X = [(3/8, (-2)/8),((-3)/8 , 4/8)]

= [(3/8 , (-1)/4),((-3)/8, 1/2)]

By (i) – (ii) x 3, we get

8Y = [(1, -1),(-1, 1)] - 3[(0, -1),(0, -1)]

= [(1, -1),(-1, 1)] - [(0, -3),(0, -3)]

= [(1 - 0, -1 + 3),(-1 - 0, 1 + 3)]

∴ 8Y = [(1, 2),(-1, 4)]

∴ Y = (1)/(8)[(1, 2),(-1, 4)]

= [(1/8, 2/8),((-1)/8, 4/8)]

= [(1/8, 1/4),((-1)/8, 1/2)].

Is there an error in this question or solution?
Chapter 2: Matrices - Exercise 2.2 [Page 47]

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