find A-1 inverse

Question

3x+3y-2z=4-

-3x+2y+3z=1

x-y-z=-2

 

a)find inverse

b)use the inverse to solve the system

Answer 1

Using the TI-84 calculator, the inverse of the coefficient matrix is  calculated to be the matrix

 

 1  5  13

0  -1  -3

1  6  15

 

Since the inverse exists, the solution to the system is obtained by multiplying the column vector

 

-4

1

-2

 

by the inverse matrix above.   This results in the column vector

 

-25

5

-28

 

So  x =  -25     y =   5   and z  =  -28

 

Notice that the 4-  in the problem statement has been changed to -4