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Question
Solve the system of linear equations using the matrix method.
5x + 2y = 3
3x + 2y = 5
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Solution
`[(5,2),(3,2)] [(x),(y)] = [(3),(5)]` AX = B
A = `[(5,2),(3,2)]`
X = `[(x),(y)]` or B = `[(3),(5)]`
Now, |A| = `|(5,2),(3,2)|`
= 10 − 6
= 4 ≠ 0
⇒ A−1 exists and hence the given equation has a minimal solution.
∴ Adj A = `[(2,-3),(-2,5)]^T = [(2,-2),(-3,5)]`
And A−1 = `1/|A|` (Adj A)
= `1/4 [(2,-2),(-3,5)]`
X = A−1B
⇒ `[(x),(y)] = 1/4 [(2,-2),(-3,5)] [(3),(5)]`
= `1/4 [(6-4), (-9 + 25)]`
= `1/4[(-4), (16)]`
= `[(-1),(4)]`
x = −1, y = 4
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