Question

Solve by matrix inversion method:

2x + 3y – 5 = 0; x – 2y + 1 = 0.

Answer 1

2x + 3y = 5

x – 2y = -1

The given system can be written as

`[(2,3),(1,-2)][(x),(y)] = [(5),(-1)]`

AX = B

where A = `[(2,3),(1,-2)]`, X = `[(x),(y)]` and B = `[(5),(-1)]`

|A| = `|(2,3),(1,-2)|` = - 4 - 3 = - 7 ≠ 0

∴ A^-1 Exists.

adj A = `[(-2,-3),(-1,2)]`

`"A"^-1 = 1/|"A"|`(adj A)

= `1/(-7)[(-2,-3),(-1,2)]`

X = A^-1B

`[(x),(y)] = -1/7[(-2,-3),(-1,2)][(5),(-1)]`

`=> -1/7[(-10+3),(-5-2)]`

`=> -1/7 [(-7),(-7)]`

`[(x),(y)] = [(1),(1)]`

∴ x = 1, y = 1