Find the inverse, if possible

Question

C=[1 0 0]

    [-2 1 0]

    [3 0 2]

   1st row=? 2nd row=? 3rd row=?

Answer 1

first row: 1 0 0

2nd row 2 1 0

3rd row -1.5 0 .5

or

l 1 0 0 l

l 2 1 0 l

l3/2 0 1/2 l is the inverse matrix

just do row operations

on an augmented matrix with diagonal 1's

1 0 0 l 1 0 0

2 1 0 l 0 1 0

3 0 2 l 0 0 1

multiply 1st row by -2 and add to 2nd row

multiply 1st row by -3 and add to 3rd row

divide 3rd row by 2 that

gives you

1 0 0 l 1 0 0

0 1 0 l 2 1 0

0 0 1 l -1.5 0 .5

you shift the 1 diagonal matrix from right side to the left side

then what's on the right side is the inverse matrix

multiply the original matrix times the inverse matrix gives the matrix with 1's on the diagonal