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12-1-1 122-1 1

Question

Find the inverse

Step by step explanation on how to perform the row operations to find the inverse.

1
2
-1
-1 1
2
2
-1 1
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1 2 -1 -1 1 2 2 -1 1

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Step 1

First we write using augmented matrix. 

-1 1 0 0
1 2
2 0 1 0
-1 1
-1 10 1
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-1 1 0 0 1 2 2 0 1 0 -1 1 -1 10 1

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Step 2

Make zeros in column 1 except the entry at row 1, column 1 (pivot entry).

Add row 1 to row 2.

Subtract row 1 multiplied by 2 from row 3

1 0 0
2
-1
0 3
11 1 0
(R2= R2+R1)
(R3 R3(2)R1)
0 -5
3
-2 0 1
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1 0 0 2 -1 0 3 11 1 0 (R2= R2+R1) (R3 R3(2)R1) 0 -5 3 -2 0 1

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Step 3

Make zeros in column 2 except the entry at row 2, column 2 (pivot entry). Divide row 2 by 3

...
-1 |1 0 O
1 2
R2
0 1
R2
0
0 -5 3-2 0 1
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-1 |1 0 O 1 2 R2 0 1 R2 0 0 -5 3-2 0 1

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Math

Algebra

Matrices

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