Question

If = `[(2"a" + "b", 3"a" - "b"),("c" + 2"d", 2"c" - "d")] = [(2, 3),(4, -1)]`, find a, b, c and d.

Answer 1

`[(2"a" + "b", 3"a" - "b"),("c" + 2"d", 2"c" - "d")] = [(2, 3),(4, -1)]`

By equality of matrices,

2a + b = 2     ...(1)

3a – b = 3   ...(2)

c + 2d = 4    ...(3)

2c – d = – 1  ...(4)

Adding (1) and (2), we get,

5a = 5

∴ a = 1

∴ from (1), b = 2 – 2a = 2 – 2 = 0

Multiplying equation (3) by 2, we get,

2c + 4d = 8

Subtracting equation (4) from this equation, we get,

5d = 9

∴d = `9/5`

∴ from (3), `"c" + 2(9/5)` = 4

∴ c = `4 - 18/5 = 2/5`

Hence, a = 1 , b = 0, c = `2/5 and "d" = 9/5`.