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Question
Express the following equations in matrix form and solve them by method of reduction.
x + 3y = 2, 3x + 5y = 4
Solution
Matrix form of the given system of equations is
`[(1, 3),(3, 5)] [(x),(y)] = [(2),(4)]`
This is of the form AX = B,
where A = `[(1, 3),(3, 5)], "X" = [(x),(y)] "and B" = [(2),(4)]`
Applying R2 → R2 – 3R1, we get
`[(1, 3),(0, -4)] [(x),(y)] = [(2),(-2)]`
Hence, the original matrix A is reduced to an upper triangular matrix.
∴ `[(x + 3y),(0 - 4y)] = [(2),(-2)]`
∴ By euality of matrices, we get
x + 3y = 2 ...(i)
– 4y = – 2 ...(ii)
From equation (ii),
y = `(1)/(2)`
Sustituting y = `(1)/(2)` in equation (i), we get
`x + 3/2` = 2
∴ x = `2 - (3)/(2) = (1)/(2)`
∴ x = `(1)/(2) "and y" =(1)/(2)` is the required soution.
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