#### 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

A_{11} = 7, A_{12} = 3, A_{13} = -1

A_{21} = -3, A_{22 }= 0, A_{23} = 3

A_{31} = 2, A_{32} = -3, A_{33} = 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?

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