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Question

The value(s) of x for which the value of detA=0, where A=⎡⎢⎣x−1111x−1111x−1⎤⎥⎦

A
1
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B
0
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C
1
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D
2
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Solution

The correct option is D 2
|A|=∣ ∣x1111x1111x1∣ ∣
Expanding along the first row
|A|=(x1)x111x11111x1+11x111
=(x1)((x1)(x1)1)1((x1)1)+1(1(x1))
=(x1)(x22x+11)(x2)+(2x)
=x(x1)(x2)(x2)(x2)
=(x2)[x(x1)2]
=(x2)(x2x2)
Now |A|=0
(x2)(x2x2)=0
(x2)(x2)(x+1)=0
x=1 or 2

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