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Question
Express the following equations in matrix form and solve them by method of reduction.
3x – y = 1, 4x + y = 6
Solution
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.
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