Answer :

= 8I_{3}

Now,

we have-

x - y + z = 4

x - 2y - 2z = 9

2x + y + 3z = 1

Writing these equations in matrix form-

⇒ AX = B

where,

If |A| ≠ 0

Then the solution of the equations by matrix method is given by-

X = A^{-1}B

Now,

Expanding along C_{1}

|A| = [(1)(-6+2)-(1)(-3-1)+(2)(2+2)] = [(1)(-4)-(1)(-4)+(2)(4)]

= [-4+4+8]

= 8

we know that-

A(adj A) = |A|I_{n} = (adj A)A

Comparing this with

we get-

.

Thus,

.

Hence,

x = 3, y = -2, z = -1

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