Question

Solve the system of linear equations using the matrix method.

5x + 2y = 3

3x + 2y = 5

Answer 1

`[(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