Question

If A = |(2, 3, 4), (1, -1, 0), (0, 1, 2),

find A^-1

Hence, solve the system of equations ; 

x - y = 3; 

2x + 3y + 4z = 17;

y + 2z = 7;

Answer 1

A = 

|A| = 2(−2) − 3(2 − 0) + 4(1 − 0) = − 6 ≠ 0

Cofactors

A₁₁ = - 2, A₁₂ = - 2, A₁₃ = 1

A₂₁ = - 2, A₂₂ = 4, A₂₃ = - 2

A₃₁ = 4, A₃₂ = 4, A₃₃ = - 5

System of equations can be written as AX = B

Where A = 

Now AX = B

X = A^-1B

x = 2, y = -1, z = 4