# If a = ⎡ ⎢ ⎣ 1 1 1 0 1 3 1 − 2 1 ⎤ ⎥ ⎦ ,Find A-1 Hence, Solve the Following System of Equations X+Y+Z = 6 Y+3z =11 X-2y+Z = 0 - Mathematics

#### Question

Sum

If A = [(1, 1, 1),(0, 1, 3),(1, -2, 1)],find A-1

hence, solve the following system of equations

x + y + z = 6
y + 3z =11
x- 2y + z = 0

#### Solution

[(1, 1, 1),(0, 1, 3),(1, -2, 1)]

Cofactors

A11 = 7, A12 = 3, A13 = -1
A21 = -3, A22 = 0, A23 = 3
A31 = 2, A32 = -3, A33 = 1

A-1 = (Adj("A")) /|"A"|

Adj (A) = [(7, 3, -1),(-3, 0, 3),(2, -3, 1)]^"T" = [(7, -3, 2),(3, 0, -3),(-1, 3, 1)]

|A| = 9

"A"^-1 = 1/9 [(7, -3, 2),(3, 0, -3),(-1, 3, 1)]

For system of equations

AX = B

X = "A"^-1 "B"

[("x"),("y"),("z")] = 1/9 [(7, -3, 2),(3, 0, -3),(-1, 3, 1)] [(6),(11),(0)]

[("x"),("y"),("z")] = 1/9 [(9),(18),(27)]

x =1, y = 2, z = 3

Is there an error in this question or solution?