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प्रश्न
Solve the system of linear equations using the matrix method.
4x – 3y = 3
3x – 5y = 7
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उत्तर
`[(4,-3),(3,-5)] [(x),(y)] = [(3),(7)]` AX = B
A = `[(4,-3),(3,-5)]`
X = `[(x),(y)]` and B = `[(3),(7)]`
Now, |A| = `[(4,-3),(3,-5)]`
= −20 + 9
= −11 ≠ 0
⇒ A−1 exists and hence the given equation has a unique solution.
∴ Adj A = `[(-5,-3),(3,4)]^T = [(-5,3),(-3,4)]`
and A−1 = `1/|A|` (Adj A)
= `1/-11 [(-5,3),(-3,4)]`
X = A−1B
⇒ `[(x),(y)] = 1/11 [(-5,-3),(3,4)] [(3),(7)]`
= `[(-6/11),(-19/11)]`
So, x = `-6/11`, y = `-19/11`
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