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प्रश्न
Solve the system of linear equations using the matrix method.
5x + 2y = 4
7x + 3y = 5
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उत्तर
The given equation,
5x + 2y = 4
7x + 3y = 5
A = `[(5,2),(7,3)]`, X = `[(x),(y)]` and B = `[(4),(5)]`
⇒ AX = B
⇒ X = A−1B
The cofactors of the elements of matrix A are as follows:
A11 = 3, A12 = −7, A21 = −2, A22 = 5
Matrix composed of the elements of the cofactor of A = `[(3,-7),(-2,5)]`
adj A = `[(3,-7),(-2,5)] = [(3,-2),(-7,5)]`
|A| = `|(5,2),(7,3)|`
= 15 − 14
= 1 ≠ 0
∴ A−1 = `1/|A|` (adj A)
= `1/1 [(3,-2),(-7,5)]`
X = A−1B = `[(3,-2),(-7,5)][(4),(5)]`
= `[(12 - 10),(-28 + 25)]`
= `[(2),(-3)]`
⇒ `[(x),(y)] = [(2),(-3)]`
⇒ x = 2 and y = −3
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