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Question

The system of equations 3x + 2y + z=6, 3x + 4y + 3z = 14, 6x + 10y + 8z = a, has infinite number of solutions, if a =

A
8
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B
12
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C
24
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D
36
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Solution

The correct option is D 36
It will have infinite soln if Δ=Δ1=Δ2=Δ3=0
Δ=∣ ∣3213436108∣ ∣=3×2∣ ∣111123258∣ ∣=6[1+(2)+1]=0
Δ1=∣ ∣6221443a108∣ ∣=6(2)+2(3a112)+1404a
Δ1=0
12+6a=224+1404a=0
2a=224152
a=11276
a=36

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