This Question: 3 pts eimination to soive the linear system and determine whether

Question

This Question: 3 pts eimination to soive the linear system and determine whether the sysltem has a unique solution, no solution, or infinely many soutions I the system -2x-y has infinitaly many solutions, describe the soution as an ordered tiple invoving a free variable Select the comet heice below and S in any anowr boxes wilthie your cholce O A There is one solution The soution Type an satt answer i, simpled brt.) ype an exact anwer in simplified fom O C. There is no sclution s lock control option command command option

Explanation / Answer

The augmented matrix of the given linear system is A =

-2

-1

3

0

4

3

2

-1

1

1

-2

-1/2

To solve the given linear system, We will reduce A to its RREf as under:

Multiply the 1st row by -1/2

Add -4 times the 1st row to the 2nd row

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

Add -1/2 times the 2nd row to the 3rd row

Multiply the 3rd row by -2/9

Add -8 times the 3rd row to the 2nd row

Add 3/2 times the 3rd row to the 1st row

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

Then the RREF of A is

1

0

0

½

0

1

0

-1

0

0

1

0

                It implies that there is only one solution which is x = ½, y = -1 and z= 0, i.e. (x,y,z) = (1/2,-1,0).

-2

-1

3

0

4

3

2

-1

1

1

-2

-1/2

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