    Question

# Consider the system of equations x+y+z=6, x+2y+3z=10 and x+2y+λz=μ Statement 1: If the system has infinite number of solutions, then μ=10. Statement 2: The value of ∣∣ ∣∣116121012μ∣∣ ∣∣=0 for μ=10.

A
Both the statements are true and Statement 2 is the correct explanation of Statement 1.
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B
Both the statements are true but Statement 2 is not the correct explanation of Statement 1.
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C
Statement 1 is true and Statement 2 is false.
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D
Statement 1 is false and Statement 2 is true.
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Solution

## The correct option is D Both the statements are true but Statement 2 is not the correct explanation of Statement 1.Let Δ=∣∣ ∣∣11112312λ∣∣ ∣∣=0⇒λ=3. Now, Δ1=∣∣ ∣∣6111023μ2λ∣∣ ∣∣ =∣∣ ∣∣6111023μ2λ∣∣ ∣∣=μ−10 (∵λ=3) Δ2=∣∣ ∣∣16111031μλ∣∣ ∣∣ =∣∣ ∣∣16111031μ3∣∣ ∣∣=20−2μ Δ3=∣∣ ∣∣116121012μ∣∣ ∣∣=μ−10 Clearly, for μ=10, all of Δ1,Δ2,Δ3 are zero.  Suggest Corrections  0      Similar questions  Explore more