The system of equations $x + y + z=5$

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Matrices

Question:

The system of equations

$x + y + z=5$

$x + 2y + 3z=9$

$x + 3y+λz =μ$

has a unique solution, if

Options:

$λ=5, μ = 13$

$λ≠5$

$λ=5, μ ≠13$

$μ ≠13$

Correct Answer:

$λ≠5$

Explanation:

The system of equations will have unique solution if

$\begin{vmatrix}1&1&1\\1&2&3\\1&3&λ\end{vmatrix}≠0⇒λ-5≠0⇒λ≠5$