SOLUTION: a. Write each linear system as a matrix equation in the form AX=B b. Solve the system using the inverse that is given for the coefficient matrix. <pre> Th

Algebra ->  Matrices-and-determiminant -> SOLUTION: a. Write each linear system as a matrix equation in the form AX=B b. Solve the system using the inverse that is given for the coefficient matrix. <pre> Th      Log On


   

Question 191482: a. Write each linear system as a matrix equation in the form AX=B
b. Solve the system using the inverse that is given for the coefficient matrix.
                     The inverse of
 x + 2y + 5z = 2            [ 1 2 5] is [ 2 -1 -1]
2x + 3y + 8z = 3            [ 2 3 8] is [12 -7 -2]
-x +  y + 2z = 3            [-1 1 2] is [-5  3  1]
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!


               A     X  =  B 
          [ 1  2  5][x]   [2]
          [ 2  3  8][y] = [3]
          [-1  1  2][z]   [3]

Left multiply both sides by A-1

    A-1        A     X  =     A-1    B 
[ 2 -1 -1][ 1  2  5][x]   [ 2 -1 -1][2]
[12 -7 -2][ 2  3  8][y] = [12 -7 -2][3]
[-5  3  1][-1  1  2][z]   [-5  3  1][3]


               I     X  =  A-1B 
          [ 1  0  0][x]   [-2]
          [ 0  1  0][y] = [-3]
          [ 0  0  1][z]   [ 2]

                     X  =  A-1B 
                    [x]   [-2]
                    [y] = [-3]
                    [z]   [ 2]

Therefore x=-2, y=-3, z=2

Edwin