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Question

If the system of linear equations
x+ay+z=3
x+2y+2z=6
x+5y+3z=b
has no solution, then:

A
a=1, b9
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B
a=1, b9
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C
a=1, b=9
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D
a1, b=9
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Solution

The correct option is A a=1, b9
For given system of linear equations which has no solution,
Case 1:
=0
∣ ∣1a1122153∣ ∣=0
1(610)a(32)+1(52)=0
a=1

Case 2:
10
∣ ∣11312615b∣ ∣0
1(2b30)+1(b6)+3(52)0
b9
Hence, a=1, b9

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