3 1 2

3 2 -1

1 1 1

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## 1 Answer

Work out the determinant: 3(2+1)-1(3+1)+2(3-2)=9-4+2=7.

Take each column and make it into a row:

3  3 1

1  2 1

2 -1 1

Replace each element with its subdeterminant:

(2×1-1×-1)=3  (1×1-1×2)=-1 (1×-1-2×2)=-5

(3×1-(-1)×1)=4 (3×1-1×2)=1 (3×-1-3×2)=-9

(3×1-1×2)=1 (3×1-1×1)=2 (3×2-3×1)=3

Change the sign of every other element and divide by the determinant:

( 3  1 -5)

(-4  1  9) ÷ 7

(1 -2  3)

Check the result by applying to the original matrix:

( 3  1 -5)(3  1  2)

(-4  1  9)(3  2 -1) ÷ 7

(1 -2  3)(1  1  1)=

(1 0 0)

(0 1 0)

(0 0 1)

The result is the identity matrix, so the inverse is correct.

by Top Rated User (660k points)

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