Question

Solve the following system of linear equations using matrix method: 
3x + y + z = 1
2x + 2z = 0
5x + y + 2z = 2

Answer 1

3x + y + z = 1
2x + 2z = 0
5x + y + 2z = 2

A=`[(3,1,1),(2,0,2),(5,1,2)] ; "X" = [("x"),("y"),("z")] ; B = [(1),(0),(2)]`

A=`[(3,1,1),(2,0,2),(5,1,2)]`

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

`"adj A" =[(-2,6,2),(-1,1,2),(2,-4,-2)]^t = [(-2,-1,2),(6,1,-4),(2,2,-2)]`

`"A"^-1=1/2 [(-2,-1,2),(6,1,-4),(2,2,-2)]`

`"X"= "A"^-1 "B"  = 1/2[(-2,-1,2),(6,1,-4),(2,2,-2)][(1),(0),(2)]`

`"X"= 1/2 [(2),(-2),(-2)] = [(1),(-1),(-1)]`

x = 1 , y = -1, z = -1.