Use the matrix transformation method to solve this system. x - 2y - 3z = -1 2x + y + z = 6 x + 3y - 2z = 13

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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We will rewrite the equations as a matrix.

 

==> 1     -2      -3   :   -1

        2      1       1    :  6

        1       3      -2   :    13

 

Now we need to transform the matrix into the form:

1   0   0   :  a

0   1   0   : b

0    0   1 : C

Such that (a, b, c) is the solution to the system.

We will use the elimination method to solve.

First we will multiply R1 by 2 and subtract from R2

==>  1    -2    -3    : -1

         0     -5    -7   :  -8

          1     3      -2  : 13    R1 - R3

 

==> 1     -2    -3  : -1

        0      -5    -7 : -8

        0      -5     -1 : -14      R2 - R3

 

==>  1    -2    -3   : -1

          0   -5     -7  : -8

          0     0     -6 :  6         Divide R3 by -6

 

==> 1     -2    -3  : -1

        0     -5     -7 : -8

        0       0      1 : -1          R2 / -5

 

==> 1    -2    -3   : -1

         0    1    7/5  : 8/5

         0     0    1    : -1           -7/5 * R3  + R2

 

==> 1    -2     -3   : -1

        0     1      0  :   3

         0     0     1    : -1          3*R3 + R1

 

==> 1    -2      0   :  -4

        0    1      0    : 3

         0    0      1   : -1            2*R2 + R1

 

==> 1     0    0   :  2

        0     1    0   : 3

        0     0     1   : -1

 

Then the solution is:

x= 2     y = 3    z = -1

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