SOLUTION express your answer in terms of twhere xtyoth and t

SOLUTION.) express your answer in terms of t,where xt),yoth, and t If there is no solution, enter NO (x, y, z) Need Help?

Solution

The given system of linear equations is x-2y-3z = 3, 2x+y-z = 3 and 4x-3y-7z = 0. The augmented matrix of this system of linear equations is A =

1

-2

-3

3

2

1

-1

3

4

-3

-7

3

To solve these equations, we will reduce A to its RREF as under:

Add -2 times the 1st row to the 2nd row

Add -4 times the 1st row to the 3rd row               

Multiply the 2nd row by 1/5

Add -5 times the 2nd row to the 3rd row

Multiply the 3rd row by -1/6

Add 3/5 times the 3rd row to the 2nd row

Add -3 times the 3rd row to the 1st row

Add 2 times the 2nd row to the 1st row

Then the RREF of A is

1

0

-1

0

0

1

1

0

0

0

0

1

Now, in view of the last row of the RREF of A, the given system of linear equations is equivalent to x-z = 0 or, z = x, y+z = 0 or, y = -z = -x and 1 = 0. Hence the given system of linear equations is inconsistent.

1	-2	-3	3
2	1	-1	3
4	-3	-7	3