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Question

If the system of equations x+ay=0, az+y=0, ax+z=0 has
infinite number of solutions then the value of a is

A
1
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B
1
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C
0
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D
No real value
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Solution

The correct option is A 1
x+ay=0(1)
az+y=0(2)
ax+z=0(3)
The above equations is a system of homogenous equations so, it will have infinite many solution if the determinant of the coefficient matrix is zero
∣ ∣1a001aa01∣ ∣=0
1(10)a(0a2)=0a3=1a=1

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