# Using the matrix transformation method, solve this system. 2x+6y-4z = 1 x+3y-2z = 4 2x+y-3z = -7

Let us write the system as a matrix:

Let A be the matrix

2    6    -4    :   1

1     3    -2   :   4

2     y      -3  : -7

We need to transform the matrix into the form :

1    0     0   :   a

0      1    0 :    b

0       0    1 :...

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Let us write the system as a matrix:

Let A be the matrix

2    6    -4    :   1

1     3    -2   :   4

2     y      -3  : -7

We need to transform the matrix into the form :

1    0     0   :   a

0      1    0 :    b

0       0    1 : C

Where a , b, c  is the solution to the system.

First we will divide  R1 by 2:

==> 1      3      -2   : 1/2

1     3       -2   : 4

2      1       -3   : -7     R1 - R2

==> 1     3     -2     : 1/2

==>   0    0      0     : -3.5

2      1     -3   : -7

We notice that the second row has cancelled, then there are no solution to the system.

Also, when looking at the first 2 equations, we notice that the second is a multiply of the first but the answers are different. which is impossible.

Then, there are are no solutions to the system.

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