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Question: Which of the following operators in R2 are linear? A. L(x)=(x1+10,x2)T B. L(x)=(8x1+x2,−x1)T C. L(x)=(3x1,4)T D. L(x)=(0,9x2)T

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Step 1
A. Given operator $L (x) = {(x_{1} + 10, x_{2})}^{T}$
Let $x = (x_{1}, x_{2}), y = (y_{1}, y_{2}) \in R^{2} and α, β \in R$
Now $L (α x + β y) = L (α x_{1} + β y_{1}, α x_{2} + β y_{2})$
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Transcribed image text:

Which of the following operators in

R^{2}

are linear? A.

L (x) = (x_{1} + 10, x_{2})^{T}

L (x) = (8 x_{1} + x_{2}, - x_{1})^{T}

L (x) = (3 x_{1}, 4)^{T}

L (x) = (0, 9 x_{2})^{T}