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Question

If (x,y,z)(0,0,0) and (^i+^j+3^k)x+(3^i3^j+^k)y+(4^i+5^j)z=λ(x^i+y^j+z^k), then the value of λ will be

A
2,0
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B
0,2
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C
1,0
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D
0,1
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Solution

The correct option is D 0,1
Comparing the coefficients of ^i,^j and ^k, the corresponding equatiion are

x+3y4z=λx

or (1λ)x+3y4z=0 ........ (i)

x(λ+3)y+5z=0 .......... (ii)

3x+yλz=0 ......... (iii)

These equation (i),(ii) and (iii) have a non-trivial solution, if
∣ ∣ ∣(1λ)341(λ+3)531λ∣ ∣ ∣=0λ=0,1

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