Question

Using matrix solve the following system of equations :

x + y + z = 6

2x + y - 3z = - 5

3x - 2y + z = 2

Answer 1

Let

= 1(1 - 6) - 1(2 + 9) + 1(-4 - 3) = -5 - 11 - 7 = -23

Co-factor of 1 = + |(1,-3),(-2,1)| = 1 - 6 = -5

Co-factor of 1 = - |(2,-3),(3,1)| = -(2 + 9) = - 11

Co-factor of 1 = + |(2,1),(3,-2)| = - 4 - 3 = -7

Co-factor of 2 = - |(1,1),(-2,1)| = -(1 + 2) = -3

Co-factor of 1 = + |(1,1),(3,1)| = 1 - 3 = -2

Co-factor of -3 = |(1,1),(3,-2)| = -(-2 - 3) = 5

Co-factor of 3 = +|(1,1),(1,-3)| = -3 - 1 = -4

Co-factor of -2 = |(1,1),(2,-3)| = -(-3 - 2) = 5

Co-factor of 1 = - |(1,1),(2,1)| = 1 -2 = -1

∴ x = 1, y = 2, z = 3