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+9 votes

Consider the following system of linear equations : $$2x_1 - x_2 + 3x_3 = 1$$ $$3x_1 + 2x_2 + 5x_3 = 2$$ $$-x_1+4x_2+x_3 = 3$$ The system of equations has

  1. no solution
  2. a unique solution
  3. more than one but a finite number of solutions
  4. an infinite number of solutions
asked in Linear Algebra by Boss (18.3k points) | 959 views

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2 Answers

+15 votes
Best answer
rank of matrix $=$ rank of augmented matrix $=$ no of unknown $=$ $3$
so unique solution..
answered by Veteran (55.9k points)
edited by
Can case C arise? If Yes, how shall we determine?

when rank of matrix = rank of augmented matrixno of unknown 

then it is infinite solutions. r < n, that is option D. I'm asking about option C
i think more than one but a finite number of solutions will never arise

as we have only 3 cases r=n,r<n and r>n
yes c option case can never arise
+5 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

answered by Loyal (7.9k points)

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