Question

Express the following equations in matrix form and solve them by method of reduction.

3x – y = 1, 4x + y = 6

Answer 1

Matrix form of the given system of equations is

`[(3, -1),(4, 1)] [(x),(y)] = [(1),(6)]`

This is of the form AX = B

Where A = `[(3, -1),(4, 1)]`, X = `[(x),(y)]` and B = `[(1),(6)]`

Applying R₁ → R₁ + R₂, we get

`[(7, 0),(4, 1)] [(x),(y)] = [(7),(6)]`

Hence, the original matrix A is reduced to a lower triangular matrix.

∴ `[(7x + 0),(4x + y)] = [(7),(6)]`

∴ By equality of matrices, we get

7x = 7           ...(i)

4x + y = 6    ...(ii)

From equation (i), x = 1

Substittutig x = 1 in equation (ii), we get

(4 × 1) + y = 6

∴ 4 + y = 6

∴ y = 6 – 4 = 2

∴ x = 1 and y = 2 is the required solution.