Find the inverse matrix (if it exists)

Question

[1 -1 1]

[0 -1 0]

[0 0 2]

(the brackets are all suppose to be combined)

 

Answer: first row=?

second row=?

third row=?

Answer 1

1. Orignial 

 1 - 1   1 

 0  -1   0 

 0  0    2 

 

 

2. Identity matrix. 

 

1  0  0 

0  1  0 

0  0  1 

 

Find pivot row 1 

 1 -1  1   |  1 0 0
 0 -1  0   |  0 1 0
 0  0  2   |  0 0 1

 

Find pivot row 2 
 1 -1 1  | 1 0  0
 0  1 0  | 0 -1 0
 0 0  2  | 0  0 1

 

Eliminate row 2 

1 0 1   | 1 -1  0
0 1 0   | 0 -1  0 
0 0 2   | 0  0  1

 

Divide 3rd row / 2 

1  0  1 |  1 -1  0
0  1  0 |  0 -1  0

0  0  1 |  0  0  1/2

 

Eliminate col 3 

1  0  0 |  1  -1  -1/2
0  1  0 |  0  -1   0
0  0  1 |  0   0   1/2

 

1  0  0 | -1  -1  1/2

0  1  0  |  0  -1   0

0  0  1  |  0   0   1/2

 

Answer: 

1  -1  -1/2

0  -1    0
0   0   1/2

 

 

 

Answer 2

A TI-84 calculator can be used to find the inverse .  It is

 

first row:      1 -1 -.5

Second row:  0 -1  0

Third row:     0  0  .5