Find the inverse of [5/2 3/-1]

Question

i need help on this......

Answer 1

Do you mean the matrix  ⌈ 5      3  ⌉

                                                    ⌊ 2      -1  ⌋  ??

 

To find the inverse of this matrix, switch the entries on the main diagonal (5 and -1) and negate the other two entries.  Then, multiply that matrix by the reciprocal of the determinant (5)(-1) - (3)(2) = -11

 

inverse =               ⌈-1      -3 ⌉       ⌈ 1/11        3/11 ⌉

                 (-1/11)                      = 

                               ⌊-2        5 ⌋       ⌊ 2/11      -5/11 ⌋

 

 

 

Answer 2

It's not clear what you mean by [5/2 3/-1]

 

The additive inverse of 5/2 is -5/2 (adding the two numbers equals zero).  The multiplicative inverse of 5/2 is 2/5 (multiplying the numbers equals one).

The additive inverse of 3/-1 is 3.  The multiplicative inverse of 3/-1 is -1/3.