Question

If `x[(2),(3)] + y[(-1),(1)] = [(10),(5)]`, find the values of x and y.

If `x[(2),(3)] + y[(-1),(1)] = [(10),(5)]`, then find the values of x and y.

Answer 1

`x [(2),(3)] + y [(-1),(1)] = [(10),(5)]`

⇒ `[(2x),(3x)] + [(-y),(y)] = [(10),(5)]`

⇒ `[(2x - y),(3x + y)] = [(10),(5)]`

Comparing the corresponding elements of these two matrices, we get:

2x – y = 10 and 3x + y = 5

Adding these two equations, we have:

5x = 15

⇒ x = 3

Now, 3x + y = 5

⇒ y = 5 – 3x

⇒ y = 5 – 9

⇒ y = –4

∴ x = 3 and y = –4