422 views

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 | 422 views

rank of matrix = rank of augmented matrix = no of unknown = 3
so unique solution..
answered by Veteran (48.3k points)
selected 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

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 Boss (7.3k points)

1
2