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CBSE Class 12 · 2016 · DeterminantsVery Short Answer

For what value of

k

, the system of linear equations

x + y + z = 2, 2 x + y - z = 3, 3 x + 2 y + k z = 4

has a unique solution?

Answer: $k \neq = 0$

Solution

A linear system

A X = B

has a unique solution exactly when the coefficient determinant is non-zero.

∣ A ∣ = 123112 1 - 1 k .

Apply

C_{2} \to C_{2} - C_{1}, C_{3} \to C_{3} - C_{1}

and expand along

R_{1}

:

∣ A ∣ = 123 0 - 1 - 1 0 - 3 k - 3 = - (k - 3) - 3 = - k .

For a unique solution

∣ A ∣ \neq = 0 \Rightarrow k \neq = 0

.

k \neq = 0

CBSE Class 12 Board · 2016 · Subjective

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