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4 Answers

Best answer
27 votes
27 votes
rank of matrix $=$ rank of augmented matrix $=$ no of unknown $=$ $3$
so unique solution..

Correct Answer: $B$
edited by
9 votes
9 votes

Determinant of matrix =14 which is non zero

If The determinant of the coefficient matrix is non zero then definitely the system of given equation has a unique solution 

 so option B

1 votes
1 votes
                                                       (B) A unique solution .

 

0 votes
0 votes

Method-1:

2

 

3

 

-1

-1

 

2

 

5

3

 

5

 

1





 

In this matrix we can clearly see that three columns are Linearly independent and 3 L.I columns in R3 space

 

So It will fill the space and Ax=b 

 

So there will be unique solution

 

If the column space is filled and Ax=0 then there will be a trivial solution

Method-2: Converting into  echelon form

After converting into echelon form we obtain augmented matrix as

2

 

0

 

0

-1

 

7

 

0

3

 

1

 

32

1

 

1

 

46

We can clear see all the columns have pivot and there is no [00..00|b] form

 

So there will be unique solution

Method-3: By using rank

rank[A] =3 and rank[A|b]=3  and number of columns =3

Therefore unique solution is possible

Answer is option-B

 

Answer:

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