Question

What is the nature of the given system of equations

`{:(x + 2y = 2),(2x + 3y = 3):}`

Options

• Consistent

• Non-consistent

• May or may not be consistent

• Not defined.

Answer 1

Consistent

Explanation:

`{:(x + 2y = 2),(2x + 3y = 3):}`

Let A = `[(1, 2),(2, 3)], x = [(2),(3)]` and B = `[(2),(3)]`

So that the given system of equations can be written as Ax = B. Now,

|A| = `1(3) - 2(2) = 3 - 4 = -1 ≠ 0`

∴ 'A' is non-singular

Thus A^–1 exist.

As a result, the given equation system is consistent.