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Question
The sum of the cost of one Economic book, one Co-operation book and one account book is ₹ 420. The total cost of an Economic book, 2 Co-operation books and an Account book is ₹ 480. Also the total cost of an Economic book, 3 Co-operation books and 2 Account books is ₹ 600. Find the cost of each book using matrix method.
Solution
Let the cost of one economic book, one co-operation book and one account book be ₹ x, ₹ y and ₹ z respectively.
According to the first condition,
x + y + z = 420
According to the second condition,
x + 2y + z = 480
According to the third condition,
x + 3y + 2z = 600
Matrix form of the above system of equations is
`[(1, 1, 1),(1, 2, 1),(1, 3, 2)][(x), (y), (z)] = [(420), (480), (600)]`
Applying R2 → R2 – R1 and R3 → R3 – R1, we get
`[(1, 1, 1),(0, 1, 0),(0, 2, 1)][(x), (y), (z)] = [(420), (60), (180)]`
Applying R3 → R3 – 2R2, we get
`[(1, 1, 1),(0, 1, 0),(0, 0, 1)][(x), (y), (z)] = [(420), (60), (60)]`
Hence, the original matrix is reduced to an upper triangular matrix.
∴ `[(x + y + z),(0 + y + 0),(0 + 0 + z)] = [(420), (60), (60)]`
∴ By equality of matrices, we get
x + y + z = 420 ...(i)
y = 60
z = 60
Substituting y = 60 and z = 60 in equation (i), we get
x + 60 + 60 = 420
∴ x = 420 – 120 = 300
∴ The cost of one economic book is ₹ 300, one co-operation book is ₹ 60 and one account book is ₹ 60.
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