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  • Confused! kindly explain, The system of equations x + 2y + 3z = 4, 2x + 3y + 4z = 5, 3x + 4y + 5z = 6 has

The system of equations x + 2y + 3z = 4, 2x + 3y + 4z = 5, 3x + 4y + 5z = 6 has

  • Option 1)

    Infinitely many solutions

  • Option 2)

    No solution 

  • Option 3)

    A unique solution

  • Option 4)

    None of these 

 

Answers (1)

best_answer

As we have learned

Solution of a non-homogeneous system of linear equations by matrix method -

If A is a singular matrix and Adj(A).b\neq 0, then the system of equations given by Ax=b has no solution

- wherein

 

 

Here     \Delta =\begin{vmatrix} 1 &2 &3 \\ 2& 3& 4\\ 3& 4& 5 \end{vmatrix}=0,

(rows are in AP with common difference 1).

                        Similarly \Deltax = \Deltay = \Deltaz = 0.

            Hence (A) is the correct answer.


Option 1)

Infinitely many solutions

Option 2)

No solution 

Option 3)

A unique solution

Option 4)

None of these 

Posted by

prateek

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